Sequence Database

A database with 662107 machine generated integer and decimal sequences.

Displaying the first 100 of 317122 results.

Sequence 42rfwqvyrnhlj

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, more...

integer, strictly-monotonic, +, A001477

a(n)=n
n≥0
1 operation
Variable
a(n)=1+a(n-1)
a(0)=0
n≥0
3 operations
Recursive
a(n)=n%50
n≥0
3 operations
Divisibility
a(n)=(2-1)*n
n≥0
5 operations
Arithmetic
a(n)=n^(2-1)
n≥0
5 operations
Power
a(n)=floor(n*ζ(n))
ζ(n)=Riemann Zeta
n≥0
5 operations
Prime
a(n)=n%P(1+n)
P(n)=Partition numbers
n≥0
6 operations
Combinatoric

Sequence buqmnzuccjoq

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, constant, monotonic, A000004

a(n)=a(n-1)
a(0)=0
n≥0
1 operation
Recursive

Sequence dgbv3olkf3toh

0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24, -25, -26, -27, -28, -29, -30, -31, -32, -33, -34, -35, -36, -37, -38, -39, -40, -41, -42, -43, -44, -45, -46, -47, -48, -49, more...

integer, strictly-monotonic, -, A001489

a(n)=-n
n≥0
2 operations
Arithmetic
a(n)=a(n-1)-1
a(0)=0
n≥0
3 operations
Recursive
a(n)=(1-n)%n
n≥1
5 operations
Divisibility
a(n)=-sqrt(n*n)
n≥0
5 operations
Power
a(n)=λ(n*n)-n
λ(n)=Liouville's function
n≥1
6 operations
Prime
a(n)=P(floor(1/n))-n
P(n)=Partition numbers
n≥1
7 operations
Combinatoric

Sequence dqjfnt5tdtf1p

1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, more...

integer, periodic-2, non-monotonic, +-, A033999

a(n)=-a(n-1)
a(0)=1
n≥0
2 operations
Recursive
a(n)=(-1)^n
n≥0
4 operations
Power
a(n)=cos(π*n)
π=3.141...
n≥0
4 operations
Trigonometric
a(n)=-a(n-1)%2
a(0)=1
n≥0
4 operations
Divisibility

Sequence xw3as224tu2qo

2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, more...

integer, periodic-2, non-monotonic, +-

a(n)=-a(n-1)
a(0)=2
n≥0
2 operations
Recursive
a(n)=round(tan(a(n-1)))
a(0)=2
n≥0
3 operations
Trigonometric
a(n)=-a(n-1)%3
a(0)=2
n≥0
4 operations
Divisibility
a(n)=(1-2)^n*2
n≥0
7 operations
Power

Sequence yv3fppyevpgxk

3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, more...

integer, periodic-2, non-monotonic, +-, A174971

a(n)=-a(n-1)
a(0)=3
n≥0
2 operations
Recursive
a(n)=-a(n-1)%4
a(0)=3
n≥0
4 operations
Divisibility
a(n)=round(tan(9*a(n-1)))
a(0)=3
n≥0
5 operations
Trigonometric
a(n)=log(1/exp(a(n-1)))
a(0)=3
n≥0
5 operations
Power

Sequence zefx4n0mxnbln

4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, more...

integer, periodic-2, non-monotonic, +-

a(n)=-a(n-1)
a(0)=4
n≥0
2 operations
Recursive
a(n)=-a(n-1)%5
a(0)=4
n≥0
4 operations
Divisibility
a(n)=round(3/sin(a(n-1)))
a(0)=4
n≥0
5 operations
Trigonometric
a(n)=log(1/exp(a(n-1)))
a(0)=4
n≥0
5 operations
Power

Sequence s1ae2qzrjrsul

5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, more...

integer, periodic-2, non-monotonic, +-

a(n)=-a(n-1)
a(0)=5
n≥0
2 operations
Recursive
a(n)=-a(n-1)%6
a(0)=5
n≥0
4 operations
Divisibility
a(n)=round(5*sin(a(n-1)))
a(0)=5
n≥0
5 operations
Trigonometric
a(n)=log(1/exp(a(n-1)))
a(0)=5
n≥0
5 operations
Power

Sequence arfihgdbhmbdh

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, more...

integer, strictly-monotonic, +, A000290

a(n)=n*n
n≥0
3 operations
Arithmetic
a(n)=n^2
n≥0
3 operations
Power
a(n)=lcm(n, n*n)
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility
a(n)=2*n-1+a(n-1)
a(0)=0
n≥0
7 operations
Recursive
a(n)=n^lpf(2*a(n-1))
a(0)=0
lpf(n)=least prime factor of n
n≥0
6 operations
Prime

Sequence alecwjo0v30gc

0, 0.6931471806, 1.0986122887, 1.3862943611, 1.6094379124, 1.7917594692, 1.9459101491, 2.0794415417, 2.1972245773, 2.302585093, 2.3978952728, 2.4849066498, 2.5649493575, 2.6390573296, 2.7080502011, 2.7725887222, 2.8332133441, 2.8903717579, 2.9444389792, 2.9957322736, 3.0445224377, 3.0910424534, 3.1354942159, 3.1780538303, 3.2188758249, 3.258096538, 3.295836866, 3.3322045102, 3.36729583, 3.4011973817, 3.4339872045, 3.4657359028, 3.4965075615, 3.5263605246, 3.5553480615, 3.5835189385, 3.6109179126, 3.6375861597, 3.6635616461, 3.6888794541, 3.7135720667, 3.7376696183, 3.7612001157, 3.7841896339, 3.8066624898, 3.8286413965, 3.8501476017, 3.8712010109, 3.8918202981, 3.9120230054, more...

decimal, strictly-monotonic, +

a(n)=log(n)
n≥1
2 operations
Power
a(n)=log(lcm(n, gpf(n)))
gpf(n)=greatest prime factor of n
lcm(a,b)=least common multiple
n≥1
5 operations
Prime

Sequence jn522a24cnwdo

0, 1, 1.4142135624, 1.7320508076, 2, 2.2360679775, 2.4494897428, 2.6457513111, 2.8284271247, 3, 3.1622776602, 3.3166247904, 3.4641016151, 3.6055512755, 3.7416573868, 3.8729833462, 4, 4.1231056256, 4.2426406871, 4.3588989435, 4.472135955, 4.582575695, 4.6904157598, 4.7958315233, 4.8989794856, 5, 5.0990195136, 5.1961524227, 5.2915026221, 5.3851648071, 5.4772255751, 5.5677643628, 5.6568542495, 5.7445626465, 5.8309518948, 5.9160797831, 6, 6.0827625303, 6.164414003, 6.2449979984, 6.3245553203, 6.4031242374, 6.4807406984, 6.5574385243, 6.6332495807, 6.7082039325, 6.7823299831, 6.8556546004, 6.9282032303, 7, more...

decimal, strictly-monotonic, +

a(n)=sqrt(n)
n≥0
2 operations
Power
a(n)=sqrt(n%p(P(n)))
P(n)=Partition numbers
p(n)=nth prime
n≥0
6 operations
Prime

Sequence co5f4i13hchai

1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, more...

integer, monotonic, +, A000142

a(n)=n*a(n-1)
a(0)=1
n≥0
3 operations
Recursive
a(n)=n!
n≥0
2 operations
Combinatoric
a(n)=lcm(n, n*a(n-1))
a(0)=1
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility
a(n)=n^(2-1)*a(n-1)
a(0)=1
n≥0
7 operations
Power
a(n)=Ω(2^n)*a(n-1)
a(0)=1
Ω(n)=max factorization terms
n≥0
6 operations
Prime

Sequence ubzrbhwhgi3jg

1, 2.7182818285, 7.3890560989, 20.0855369232, 54.5981500331, 148.4131591026, 403.4287934927, 1096.6331584285, 2980.9579870417, 8103.0839275754, 22026.4657948067, 59874.1417151978, 162754.7914190039, 442413.3920089205, 1202604.2841647768, 3269017.3724721107, 8886110.520507872, 24154952.7535753, 65659969.13733051, 178482300.96318725, 485165195.4097903, 1318815734.4832146, 3584912846.131592, 9744803446.248903, 26489122129.84347, 72004899337.38588, more...

decimal, strictly-monotonic, +

a(n)=exp(n)
n≥0
2 operations
Power
a(n)=exp(n%p(P(n)))
P(n)=Partition numbers
p(n)=nth prime
n≥0
6 operations
Prime

Sequence umplcbnlhplyn

0, -1, -3, -6, -10, -15, -21, -28, -36, -45, -55, -66, -78, -91, -105, -120, -136, -153, -171, -190, -210, -231, -253, -276, -300, -325, -351, -378, -406, -435, -465, -496, -528, -561, -595, -630, -666, -703, -741, -780, -820, -861, -903, -946, -990, -1035, -1081, -1128, -1176, -1225, more...

integer, strictly-monotonic, -

a(n)=a(n-1)-n
a(0)=0
n≥0
3 operations
Recursive
a(n)=(1-n)/(2/n)
n≥1
7 operations
Arithmetic
a(n)=a(n-1)^(2-1)-n
a(0)=0
n≥0
7 operations
Power
a(n)=a(n-1)-n%(1+n)
a(0)=0
n≥0
7 operations
Divisibility
a(n)=a(n-1)-n%p(p(n))
a(0)=0
p(n)=nth prime
n≥0
7 operations
Prime

Sequence dnb1wejvpehll

0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, more...

integer, monotonic, +, A110654

a(n)=n-a(n-1)
a(0)=0
n≥0
3 operations
Recursive
a(n)=ceil(n/2)
n≥0
4 operations
Arithmetic
a(n)=n%2+a(n-1)
a(0)=0
n≥0
5 operations
Divisibility
a(n)=floor(ζ(a(n-1))+a(n-2))
a(0)=0
a(1)=1
ζ(n)=Riemann Zeta
n≥0
5 operations
Prime
a(n)=n-a(n-1)%P(n)
a(0)=0
P(n)=Partition numbers
n≥0
6 operations
Combinatoric
a(n)=n^(2-1)-a(n-1)
a(0)=0
n≥0
7 operations
Power

Sequence vtsqmvu022mjo

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, more...

integer, strictly-monotonic, +, A000217

a(n)=n+a(n-1)
a(0)=0
n≥0
3 operations
Recursive
a(n)=(1+n)/2*n
n≥0
7 operations
Arithmetic
a(n)=n^2-a(n-1)
a(0)=0
n≥0
5 operations
Power
a(n)=n%(1+n)+a(n-1)
a(0)=0
n≥0
7 operations
Divisibility
a(n)=n+a(n-1)%p(a(n-1))
a(0)=0
p(n)=nth prime
n≥0
6 operations
Prime

Sequence hndi1jkl020kk

1, 0, -2, -5, -9, -14, -20, -27, -35, -44, -54, -65, -77, -90, -104, -119, -135, -152, -170, -189, -209, -230, -252, -275, -299, -324, -350, -377, -405, -434, -464, -495, -527, -560, -594, -629, -665, -702, -740, -779, -819, -860, -902, -945, -989, -1034, -1080, -1127, -1175, -1224, more...

integer, strictly-monotonic, +-

a(n)=a(n-1)-n
a(0)=1
n≥0
3 operations
Recursive
a(n)=2-n^2-a(n-1)
a(0)=1
n≥0
7 operations
Power
a(n)=a(n-1)-n%(1+n)
a(0)=1
n≥0
7 operations
Divisibility
a(n)=a(n-1)-n%p(p(n))
a(0)=1
p(n)=nth prime
n≥0
7 operations
Prime

Sequence spwfakucb0xrj

1, 0, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10, 12, 11, 13, 12, 14, 13, 15, 14, 16, 15, 17, 16, 18, 17, 19, 18, 20, 19, 21, 20, 22, 21, 23, 22, 24, 23, 25, 24, more...

integer, non-monotonic, +, A028242

a(n)=n-a(n-1)
a(0)=1
n≥0
3 operations
Recursive
a(n)=n%(1+n)-a(n-1)
a(0)=1
n≥0
7 operations
Divisibility
a(n)=n^(2-1)-a(n-1)
a(0)=1
n≥0
7 operations
Power
a(n)=floor(ζ(a(n-1))+a(n-2))
a(0)=1
a(1)=0
ζ(n)=Riemann Zeta
n≥0
5 operations
Prime

Sequence wgwdb1qwuvh0p

1, 1, 0.5, 0.1666666667, 0.0416666667, 0.0083333333, 0.0013888889, 0.0001984127, 0.0000248016, 0.0000027557, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

decimal, monotonic, +

a(n)=a(n-1)/n
a(0)=1
n≥0
3 operations
Recursive
a(n)=n^(1-2)*a(n-1)
a(0)=1
n≥0
7 operations
Power
a(n)=a(n-1)/n%(1+n)
a(0)=1
n≥0
7 operations
Divisibility
a(n)=a(n-1)/n%p(p(n))
a(0)=1
p(n)=nth prime
n≥0
7 operations
Prime

Sequence jr4rnjjykisqj

1, 1, 2, 1.5, 2.6666666667, 1.875, 3.2, 2.1875, 3.6571428571, 2.4609375, 4.0634920635, 2.70703125, 4.4329004329, 2.9326171875, 4.7738927739, 3.1420898438, 5.0921522922, 3.338470459, 5.3916906623, 3.52394104, 5.675463855, 3.700138092, 5.9457240386, 3.8683261871, 6.2042337794, 4.0295064449, 6.4524031306, 4.184487462, 6.6913810243, 4.3339334428, 6.922118301, 4.4783978909, 7.1454124398, 4.618347825, 7.3619400894, 4.7541815846, 7.5722812349, 4.8862421841, 7.7769374845, 5.0148275048, 7.9763461379, 5.1401981924, 8.1708911657, 5.2625838637, 8.3609118904, 5.3821880424, 8.5467099324, 5.4991921302, 8.7285548246, 5.613758633, more...

decimal, non-monotonic, +

a(n)=n/a(n-1)
a(0)=1
n≥0
3 operations
Recursive
a(n)=n%(1+n)/a(n-1)
a(0)=1
n≥0
7 operations
Divisibility
a(n)=n^(2-1)/a(n-1)
a(0)=1
n≥0
7 operations
Power
a(n)=n%p(p(n))/a(n-1)
a(0)=1
p(n)=nth prime
n≥0
7 operations
Prime

Sequence mpt42acs3gazp

1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436, 466, 497, 529, 562, 596, 631, 667, 704, 742, 781, 821, 862, 904, 947, 991, 1036, 1082, 1129, 1177, 1226, more...

integer, strictly-monotonic, +, A000124

a(n)=n+a(n-1)
a(0)=1
n≥0
3 operations
Recursive
a(n)=2+n^2-a(n-1)
a(0)=1
n≥0
7 operations
Power
a(n)=n%(1+n)+a(n-1)
a(0)=1
n≥0
7 operations
Divisibility
a(n)=(n+a(n-1))%p(a(n-1))
a(0)=1
p(n)=nth prime
n≥0
6 operations
Prime

Sequence lyijhnkbtmf5p

2, -1, 3, 0, 4, 1, 5, 2, 6, 3, 7, 4, 8, 5, 9, 6, 10, 7, 11, 8, 12, 9, 13, 10, 14, 11, 15, 12, 16, 13, 17, 14, 18, 15, 19, 16, 20, 17, 21, 18, 22, 19, 23, 20, 24, 21, 25, 22, 26, 23, more...

integer, non-monotonic, +-

a(n)=n-a(n-1)
a(0)=2
n≥0
3 operations
Recursive

Sequence 5s5vbqnwckgek

2, 0.5, 4, 0.75, 5.3333333333, 0.9375, 6.4, 1.09375, 7.3142857143, 1.23046875, 8.126984127, 1.353515625, 8.8658008658, 1.4663085938, 9.5477855478, 1.5710449219, 10.1843045843, 1.6692352295, 10.7833813246, 1.76197052, 11.3509277101, 1.850069046, 11.8914480772, 1.9341630936, 12.4084675588, 2.0147532225, 12.9048062612, 2.092243731, 13.3827620486, 2.1669667214, 13.844236602, 2.2391989455, 14.2908248795, 2.3091739125, 14.7238801789, 2.3770907923, 15.1445624697, 2.4431210921, 15.5538749689, 2.5074137524, 15.9526922758, 2.5700990962, 16.3417823313, 2.6312919318, 16.7218237809, 2.6910940212, 17.0934198649, 2.7495960651, 17.4571096492, 2.8068793165, more...

decimal, non-monotonic, +

a(n)=n/a(n-1)
a(0)=2
n≥0
3 operations
Recursive
a(n)=n%(1+n)/a(n-1)
a(0)=2
n≥0
7 operations
Divisibility
a(n)=n^(2-1)/a(n-1)
a(0)=2
n≥0
7 operations
Power
a(n)=n%p(p(n))/a(n-1)
a(0)=2
p(n)=nth prime
n≥0
7 operations
Prime

Sequence xbc4ucyt4ps4m

2, 1, -1, -4, -8, -13, -19, -26, -34, -43, -53, -64, -76, -89, -103, -118, -134, -151, -169, -188, -208, -229, -251, -274, -298, -323, -349, -376, -404, -433, -463, -494, -526, -559, -593, -628, -664, -701, -739, -778, -818, -859, -901, -944, -988, -1033, -1079, -1126, -1174, -1223, more...

integer, strictly-monotonic, +-

a(n)=a(n-1)-n
a(0)=2
n≥0
3 operations
Recursive
a(n)=a(n-1)%(2*a(n-1))-n
a(0)=2
n≥0
7 operations
Divisibility
a(n)=a(n-1)^2/a(n-1)-n
a(0)=2
n≥0
7 operations
Power

Sequence f5whuvswo0daj

2, 2, 1, 0.3333333333, 0.0833333333, 0.0166666667, 0.0027777778, 0.0003968254, 0.0000496032, 0.0000055115, 0.0000005511, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

decimal, monotonic, +

a(n)=a(n-1)/n
a(0)=2
n≥0
3 operations
Recursive
a(n)=a(n-1)^2/n/a(n-1)
a(0)=2
n≥0
7 operations
Power

Sequence vthjrkdmos3qp

2, 2, 4, 12, 48, 240, 1440, 10080, 80640, 725760, 7257600, 79833600, 958003200, 12454041600, more...

integer, monotonic, +, A208529

a(n)=n*a(n-1)
a(0)=2
n≥0
3 operations
Recursive
a(n)=2*n!
n≥0
4 operations
Combinatoric
a(n)=n*lcm(a(n-1), 2)
a(0)=2
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility
a(n)=n^2/(n/a(n-1))
a(0)=2
n≥0
7 operations
Power
a(n)=Ω(2^n)*a(n-1)
a(0)=2
Ω(n)=max factorization terms
n≥0
6 operations
Prime

Sequence ul4ltexklmrij

2, 3, 5, 8, 12, 17, 23, 30, 38, 47, 57, 68, 80, 93, 107, 122, 138, 155, 173, 192, 212, 233, 255, 278, 302, 327, 353, 380, 408, 437, 467, 498, 530, 563, 597, 632, 668, 705, 743, 782, 822, 863, 905, 948, 992, 1037, 1083, 1130, 1178, 1227, more...

integer, strictly-monotonic, +

a(n)=n+a(n-1)
a(0)=2
n≥0
3 operations
Recursive
a(n)=n%a(n-1)+a(n-1)
a(0)=2
n≥0
5 operations
Divisibility
a(n)=n+a(n-1)^2/a(n-1)
a(0)=2
n≥0
7 operations
Power
a(n)=(n+a(n-1))%p(a(n-1))
a(0)=2
p(n)=nth prime
n≥0
6 operations
Prime

Sequence 4h03i2acbvrum

3, -2, 4, -1, 5, 0, 6, 1, 7, 2, 8, 3, 9, 4, 10, 5, 11, 6, 12, 7, 13, 8, 14, 9, 15, 10, 16, 11, 17, 12, 18, 13, 19, 14, 20, 15, 21, 16, 22, 17, 23, 18, 24, 19, 25, 20, 26, 21, 27, 22, more...

integer, non-monotonic, +-

a(n)=n-a(n-1)
a(0)=3
n≥0
3 operations
Recursive

Sequence jtgdaw2bxwshd

3, 0.3333333333, 6, 0.5, 8, 0.625, 9.6, 0.7291666667, 10.9714285714, 0.8203125, 12.1904761905, 0.90234375, 13.2987012987, 0.9775390625, 14.3216783217, 1.0473632813, 15.2764568765, 1.1128234863, 16.1750719868, 1.1746470133, 17.0263915651, 1.233379364, 17.8371721158, 1.2894420624, 18.6127013382, 1.343168815, 19.3572093918, 1.394829154, 20.0741430729, 1.4446444809, 20.766354903, 1.492799297, 21.4362373193, 1.539449275, 22.0858202683, 1.5847271949, 22.7168437046, 1.6287473947, 23.3308124534, 1.6716091683, 23.9290384137, 1.7133993975, 24.512673497, 1.7541946212, 25.0827356713, 1.7940626808, 25.6401297973, 1.8330640434, 26.1856644739, 1.8712528777, more...

decimal, non-monotonic, +

a(n)=n/a(n-1)
a(0)=3
n≥0
3 operations
Recursive

Sequence yw1uxhc1cwl5b

3, 2, 0, -3, -7, -12, -18, -25, -33, -42, -52, -63, -75, -88, -102, -117, -133, -150, -168, -187, -207, -228, -250, -273, -297, -322, -348, -375, -403, -432, -462, -493, -525, -558, -592, -627, -663, -700, -738, -777, -817, -858, -900, -943, -987, -1032, -1078, -1125, -1173, -1222, more...

integer, strictly-monotonic, +-

a(n)=a(n-1)-n
a(0)=3
n≥0
3 operations
Recursive

Sequence foknwmirzh1ib

3, 3, 1.5, 0.5, 0.125, 0.025, 0.0041666667, 0.0005952381, 0.0000744048, 0.0000082672, 0.0000008267, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

decimal, monotonic, +

a(n)=a(n-1)/n
a(0)=3
n≥0
3 operations
Recursive

Sequence yokycpzo01z4e

3, 3, 6, 18, 72, 360, 2160, 15120, 120960, 1088640, 10886400, 119750400, 1437004800, 18681062400, more...

integer, monotonic, +, A052560

a(n)=n*a(n-1)
a(0)=3
n≥0
3 operations
Recursive
a(n)=3*n!
n≥0
4 operations
Combinatoric
a(n)=n*lcm(a(n-1), 3)
a(0)=3
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility

Sequence igwhwuompxban

3, 4, 6, 9, 13, 18, 24, 31, 39, 48, 58, 69, 81, 94, 108, 123, 139, 156, 174, 193, 213, 234, 256, 279, 303, 328, 354, 381, 409, 438, 468, 499, 531, 564, 598, 633, 669, 706, 744, 783, 823, 864, 906, 949, 993, 1038, 1084, 1131, 1179, 1228, more...

integer, strictly-monotonic, +, A152950

a(n)=n+a(n-1)
a(0)=3
n≥0
3 operations
Recursive
a(n)=n%a(n-1)+a(n-1)
a(0)=3
n≥0
5 operations
Divisibility
a(n)=(n+a(n-1))%(a(n-1)^2)
a(0)=3
n≥0
7 operations
Power

Sequence pv2vzbuyeyojj

4, -3, 5, -2, 6, -1, 7, 0, 8, 1, 9, 2, 10, 3, 11, 4, 12, 5, 13, 6, 14, 7, 15, 8, 16, 9, 17, 10, 18, 11, 19, 12, 20, 13, 21, 14, 22, 15, 23, 16, 24, 17, 25, 18, 26, 19, 27, 20, 28, 21, more...

integer, non-monotonic, +-

a(n)=n-a(n-1)
a(0)=4
n≥0
3 operations
Recursive

Sequence oltgd5edhuklc

4, 0.25, 8, 0.375, 10.6666666667, 0.46875, 12.8, 0.546875, 14.6285714286, 0.615234375, 16.253968254, 0.6767578125, 17.7316017316, 0.7331542969, 19.0955710956, 0.7855224609, 20.3686091686, 0.8346176147, 21.5667626491, 0.88098526, 22.7018554201, 0.925034523, 23.7828961544, 0.9670815468, 24.8169351176, 1.0073766112, 25.8096125224, 1.0461218655, 26.7655240973, 1.0834833607, 27.6884732041, 1.1195994727, 28.581649759, 1.1545869563, 29.4477603578, 1.1885453961, 30.2891249394, 1.221560546, 31.1077499378, 1.2537068762, 31.9053845516, 1.2850495481, 32.6835646626, 1.3156459659, 33.4436475617, 1.3455470106, 34.1868397298, 1.3747980326, 34.9142192985, 1.4034396582, more...

decimal, non-monotonic, +

a(n)=n/a(n-1)
a(0)=4
n≥0
3 operations
Recursive

Sequence fydmgbr1xltee

4, 3, 1, -2, -6, -11, -17, -24, -32, -41, -51, -62, -74, -87, -101, -116, -132, -149, -167, -186, -206, -227, -249, -272, -296, -321, -347, -374, -402, -431, -461, -492, -524, -557, -591, -626, -662, -699, -737, -776, -816, -857, -899, -942, -986, -1031, -1077, -1124, -1172, -1221, more...

integer, strictly-monotonic, +-

a(n)=a(n-1)-n
a(0)=4
n≥0
3 operations
Recursive

Sequence 4b4kknkyn2kog

4, 4, 2, 0.6666666667, 0.1666666667, 0.0333333333, 0.0055555556, 0.0007936508, 0.0000992063, 0.0000110229, 0.0000011023, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

decimal, monotonic, +

a(n)=a(n-1)/n
a(0)=4
n≥0
3 operations
Recursive

Sequence iabkx1k1uw4ui

4, 4, 8, 24, 96, 480, 2880, 20160, 161280, 1451520, 14515200, 159667200, 1916006400, 24908083200, more...

integer, monotonic, +

a(n)=n*a(n-1)
a(0)=4
n≥0
3 operations
Recursive
a(n)=4*n!
n≥0
4 operations
Combinatoric
a(n)=n*lcm(a(n-1), 2)
a(0)=4
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility

Sequence rf05oegps3fwd

4, 5, 7, 10, 14, 19, 25, 32, 40, 49, 59, 70, 82, 95, 109, 124, 140, 157, 175, 194, 214, 235, 257, 280, 304, 329, 355, 382, 410, 439, 469, 500, 532, 565, 599, 634, 670, 707, 745, 784, 824, 865, 907, 950, 994, 1039, 1085, 1132, 1180, 1229, more...

integer, strictly-monotonic, +, A145018

a(n)=n+a(n-1)
a(0)=4
n≥0
3 operations
Recursive
a(n)=n%a(n-1)+a(n-1)
a(0)=4
n≥0
5 operations
Divisibility

Sequence xmhui2mxogfhm

5, -4, 6, -3, 7, -2, 8, -1, 9, 0, 10, 1, 11, 2, 12, 3, 13, 4, 14, 5, 15, 6, 16, 7, 17, 8, 18, 9, 19, 10, 20, 11, 21, 12, 22, 13, 23, 14, 24, 15, 25, 16, 26, 17, 27, 18, 28, 19, 29, 20, more...

integer, non-monotonic, +-

a(n)=n-a(n-1)
a(0)=5
n≥0
3 operations
Recursive

Sequence cu3zhdgy4g2vp

5, 0.2, 10, 0.3, 13.3333333333, 0.375, 16, 0.4375, 18.2857142857, 0.4921875, 20.3174603175, 0.54140625, 22.1645021645, 0.5865234375, 23.8694638695, 0.6284179687, 25.4607614608, 0.6676940918, 26.9584533114, 0.704788208, 28.3773192752, 0.7400276184, 29.728620193, 0.7736652374, 31.0211688971, 0.805901289, 32.2620156529, 0.8368974924, 33.4569051216, 0.8667866886, 34.6105915051, 0.8956795782, 35.7270621988, 0.923669565, 36.8097004472, 0.9508363169, 37.8614061743, 0.9772484368, 38.8846874223, 1.002965501, 39.8817306895, 1.0280396385, 40.8544558283, 1.0525167727, 41.8045594522, 1.0764376085, 42.7335496622, 1.099838426, 43.6427741231, 1.1227517266, more...

decimal, non-monotonic, +

a(n)=n/a(n-1)
a(0)=5
n≥0
3 operations
Recursive

Sequence 2trymnzjmmefh

5, 4, 2, -1, -5, -10, -16, -23, -31, -40, -50, -61, -73, -86, -100, -115, -131, -148, -166, -185, -205, -226, -248, -271, -295, -320, -346, -373, -401, -430, -460, -491, -523, -556, -590, -625, -661, -698, -736, -775, -815, -856, -898, -941, -985, -1030, -1076, -1123, -1171, -1220, more...

integer, strictly-monotonic, +-

a(n)=a(n-1)-n
a(0)=5
n≥0
3 operations
Recursive

Sequence tghksqjfp1flf

5, 5, 2.5, 0.8333333333, 0.2083333333, 0.0416666667, 0.0069444444, 0.0009920635, 0.0001240079, 0.0000137787, 0.0000013779, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

decimal, monotonic, +

a(n)=a(n-1)/n
a(0)=5
n≥0
3 operations
Recursive

Sequence owezdnofvqzrh

5, 5, 10, 30, 120, 600, 3600, 25200, 201600, 1814400, 18144000, 199584000, 2395008000, 31135104000, more...

integer, monotonic, +

a(n)=n*a(n-1)
a(0)=5
n≥0
3 operations
Recursive
a(n)=5*n!
n≥0
4 operations
Combinatoric
a(n)=n*lcm(a(n-1), 5)
a(0)=5
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility

Sequence spgub3wpte1il

5, 6, 8, 11, 15, 20, 26, 33, 41, 50, 60, 71, 83, 96, 110, 125, 141, 158, 176, 195, 215, 236, 258, 281, 305, 330, 356, 383, 411, 440, 470, 501, 533, 566, 600, 635, 671, 708, 746, 785, 825, 866, 908, 951, 995, 1040, 1086, 1133, 1181, 1230, more...

integer, strictly-monotonic, +

a(n)=n+a(n-1)
a(0)=5
n≥0
3 operations
Recursive
a(n)=n%a(n-1)+a(n-1)
a(0)=5
n≥0
5 operations
Divisibility

Sequence 20kztluqqh1i

0, 0.8414709848, 0.9092974268, 0.1411200081, -0.7568024953, -0.9589242747, -0.2794154982, 0.6569865987, 0.9893582466, 0.4121184852, -0.5440211109, -0.9999902066, -0.536572918, 0.4201670368, 0.9906073557, 0.6502878402, -0.2879033167, -0.9613974919, -0.7509872468, 0.1498772097, 0.9129452507, 0.8366556385, -0.0088513093, -0.8462204042, -0.905578362, -0.1323517501, 0.7625584505, 0.9563759284, 0.2709057883, -0.6636338842, -0.9880316241, -0.4040376453, 0.5514266812, 0.9999118601, 0.5290826861, -0.4281826695, -0.9917788534, -0.6435381334, 0.2963685787, 0.9637953863, 0.7451131605, -0.1586226688, -0.9165215479, -0.8317747426, 0.0177019251, 0.8509035245, 0.9017883476, 0.1235731227, -0.7682546613, -0.9537526528, more...

decimal, non-monotonic, +-

a(n)=sin(n)
n≥0
2 operations
Trigonometric

Sequence 2meyuegu0uzbn

0, 1.5574077247, -2.1850398633, -0.1425465431, 1.1578212823, -3.3805150062, -0.2910061914, 0.8714479827, -6.7997114552, -0.4523156594, 0.6483608275, -225.9508464542, -0.6358599287, 0.4630211329, 7.2446066161, -0.8559934009, 0.300632242, 3.4939156455, -1.1373137123, 0.1515894706, 2.2371609442, -1.5274985276, 0.008851656, 1.5881530834, -2.1348966977, -0.133526407, 1.1787535542, -3.2737038004, -0.2814296046, 0.8871428438, -6.4053311966, -0.441695568, 0.6610060415, -75.3130148001, -0.6234989627, 0.4738147204, 7.7504709057, -0.8407712554, 0.310309661, 3.6145544071, -1.1172149309, 0.1606566987, 2.2913879924, -1.4983873389, 0.0177046993, 1.6197751905, -2.0866135311, -0.1245275681, 1.2001272431, -3.1729085522, more...

decimal, non-monotonic, +-

a(n)=tan(n)
n≥0
2 operations
Trigonometric

Sequence fikvnefgblguh

1, 0.5403023059, -0.4161468365, -0.9899924966, -0.6536436209, 0.2836621855, 0.9601702867, 0.7539022543, -0.1455000338, -0.9111302619, -0.8390715291, 0.004425698, 0.8438539587, 0.9074467815, 0.1367372182, -0.7596879129, -0.9576594803, -0.2751633381, 0.6603167082, 0.9887046182, 0.4080820618, -0.5477292602, -0.9999608264, -0.5328330203, 0.4241790073, 0.9912028119, 0.6469193223, -0.2921388087, -0.9626058663, -0.7480575297, 0.1542514499, 0.9147423578, 0.8342233605, -0.0132767472, -0.8485702748, -0.9036922051, -0.1279636896, 0.7654140519, 0.955073644, 0.2666429324, -0.6669380617, -0.9873392775, -0.399985315, 0.5551133015, 0.9998433086, 0.5253219888, -0.4321779449, -0.9923354692, -0.6401443395, 0.3005925437, more...

decimal, non-monotonic, +-

a(n)=cos(n)
n≥0
2 operations
Trigonometric

Sequence dwrbbizvnafqp

0, -1, -4, -9, -16, -25, -36, -49, -64, -81, -100, -121, -144, -169, -196, -225, -256, -289, -324, -361, -400, -441, -484, -529, -576, -625, -676, -729, -784, -841, -900, -961, -1024, -1089, -1156, -1225, -1296, -1369, -1444, -1521, -1600, -1681, -1764, -1849, -1936, -2025, -2116, -2209, -2304, -2401, more...

integer, strictly-monotonic, -

a(n)=n*-n
n≥0
4 operations
Arithmetic
a(n)=-n^2
n≥0
4 operations
Power
a(n)=1-2*n+a(n-1)
a(0)=0
n≥0
7 operations
Recursive

Sequence 1r0kz5stvechb

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 1, 1, 6, 15, 20, 15, 6, 1, 1, 7, 21, 35, 35, 21, 7, 1, 1, 8, 28, 56, 70, 56, 28, 8, 1, 1, 9, 36, 84, 126, more...

integer, non-monotonic, +, A007318

a(n)=pt(n)
pt(n)=Pascals triangle by rows
n≥0
2 operations
Combinatoric
a(n)=pt(n%p(P(n)))
P(n)=Partition numbers
p(n)=nth prime
pt(n)=Pascals triangle by rows
n≥0
6 operations
Prime

Sequence zu20zaw4iq45h

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310, 14883, 17977, 21637, 26015, 31185, 37338, 44583, 53174, 63261, 75175, 89134, 105558, 124754, 147273, 173525, more...

integer, monotonic, +, A000041

a(n)=P(n)
P(n)=Partition numbers
n≥0
2 operations
Combinatoric
a(n)=P(n%p(a(n-1)))
a(0)=1
p(n)=nth prime
P(n)=Partition numbers
n≥0
5 operations
Prime

Sequence itkew3s5ydcwb

1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, more...

integer, monotonic, +, A000108

a(n)=catalan(n)
n≥0
2 operations
Combinatoric

Sequence hj1tqzyoyo4vc

2, 1.4142135624, 1.189207115, 1.0905077327, 1.0442737824, 1.0218971487, 1.0108892861, 1.0054299011, 1.0027112751, 1.0013547199, 1.0006771307, 1.0003385081, 1.0001692397, 1.0000846163, 1.0000423072, 1.0000211534, 1.0000105766, 1.0000052883, 1.0000026442, 1.0000013221, 1.000000661, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, more...

decimal, strictly-monotonic, +

a(n)=sqrt(a(n-1))
a(0)=2
n≥0
2 operations
Power

Sequence ym31nhhm4tsdm

3, 1.7320508076, 1.316074013, 1.1472026904, 1.0710754831, 1.0349277671, 1.0173139963, 1.0086198473, 1.0043006757, 1.0021480308, 1.0010734393, 1.0005365757, 1.0002682519, 1.0001341169, 1.0000670562, 1.0000335275, 1.0000167636, 1.0000083818, 1.0000041909, 1.0000020954, 1.0000010477, 1.0000005239, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, more...

decimal, strictly-monotonic, +

a(n)=sqrt(a(n-1))
a(0)=3
n≥0
2 operations
Power

Sequence 4ltn4tpjed00m

4, 2, 1.4142135624, 1.189207115, 1.0905077327, 1.0442737824, 1.0218971487, 1.0108892861, 1.0054299011, 1.0027112751, 1.0013547199, 1.0006771307, 1.0003385081, 1.0001692397, 1.0000846163, 1.0000423072, 1.0000211534, 1.0000105766, 1.0000052883, 1.0000026442, 1.0000013221, 1.000000661, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, more...

decimal, strictly-monotonic, +

a(n)=sqrt(a(n-1))
a(0)=4
n≥0
2 operations
Power

Sequence 4yfgbmicykvq

5, 2.2360679775, 1.4953487812, 1.222844545, 1.105823017, 1.0515811985, 1.0254663322, 1.0126531154, 1.0063066707, 1.0031483792, 1.0015729525, 1.0007861672, 1.0003930064, 1.0001964839, 1.0000982371, 1.0000491174, 1.0000245584, 1.0000122791, 1.0000061395, 1.0000030698, 1.0000015349, 1.0000007674, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, more...

decimal, strictly-monotonic, +

a(n)=sqrt(a(n-1))
a(0)=5
n≥0
2 operations
Power

Sequence 1zhyi1t2v40zo

0, 1, -1, 2, -3, 5, -8, 13, -21, 34, -55, 89, -144, 233, -377, 610, -987, 1597, -2584, 4181, -6765, 10946, -17711, 28657, -46368, 75025, -121393, 196418, -317811, 514229, -832040, 1346269, -2178309, 3524578, -5702887, 9227465, -14930352, 24157817, -39088169, 63245986, -102334155, 165580141, -267914296, 433494437, -701408733, 1134903170, -1836311903, 2971215073, -4807526976, 7778742049, more...

integer, non-monotonic, +-

a(n)=a(n-2)-a(n-1)
a(0)=0
a(1)=1
n≥0
3 operations
Recursive
a(n)=a(n-2)^(2-1)-a(n-1)
a(0)=0
a(1)=1
n≥0
7 operations
Power
a(n)=a(n-2)%(2*a(n-1))-a(n-1)
a(0)=0
a(1)=1
n≥0
7 operations
Divisibility

Sequence kwz2k32shxu1n

0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, more...

integer, periodic-6, non-monotonic, +-, A128834

a(n)=a(n-1)-a(n-2)
a(0)=0
a(1)=1
n≥0
3 operations
Recursive
a(n)=a(n-1)%2-a(n-2)
a(0)=0
a(1)=1
n≥0
5 operations
Divisibility
a(n)=a(n-1)^3-a(n-2)
a(0)=0
a(1)=1
n≥0
5 operations
Power
a(n)=round(sin(a(n-1)-a(n-2)))
a(0)=0
a(1)=1
n≥0
5 operations
Trigonometric

Sequence 0s52wnlrtxcdm

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, 165580141, 267914296, 433494437, 701408733, 1134903170, 1836311903, 2971215073, 4807526976, 7778742049, more...

integer, monotonic, +, A000045

a(n)=a(n-1)+a(n-2)
a(0)=0
a(1)=1
n≥0
3 operations
Recursive
a(n)=a(n-1)^(2-1)+a(n-2)
a(0)=0
a(1)=1
n≥0
7 operations
Power
a(n)=a(n-1)%(1+a(n-1))+a(n-2)
a(0)=0
a(1)=1
n≥0
7 operations
Divisibility

Sequence zelr4lvgyc1vl

0, 2, -2, 4, -6, 10, -16, 26, -42, 68, -110, 178, -288, 466, -754, 1220, -1974, 3194, -5168, 8362, -13530, 21892, -35422, 57314, -92736, 150050, -242786, 392836, -635622, 1028458, -1664080, 2692538, -4356618, 7049156, -11405774, 18454930, -29860704, 48315634, -78176338, 126491972, -204668310, 331160282, -535828592, 866988874, -1402817466, 2269806340, -3672623806, 5942430146, -9615053952, 15557484098, more...

integer, non-monotonic, +-

a(n)=a(n-2)-a(n-1)
a(0)=0
a(1)=2
n≥0
3 operations
Recursive

Sequence pwyanmbd2hpzo

0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, more...

integer, periodic-6, non-monotonic, +-

a(n)=a(n-1)-a(n-2)
a(0)=0
a(1)=2
n≥0
3 operations
Recursive
a(n)=a(n-1)%3-a(n-2)
a(0)=0
a(1)=2
n≥0
5 operations
Divisibility
a(n)=round(a(n-1)+tan(a(n-2)))
a(0)=0
a(1)=2
n≥0
5 operations
Trigonometric

Sequence gmivmeguy2iwb

0, 2, 2, 4, 6, 10, 16, 26, 42, 68, 110, 178, 288, 466, 754, 1220, 1974, 3194, 5168, 8362, 13530, 21892, 35422, 57314, 92736, 150050, 242786, 392836, 635622, 1028458, 1664080, 2692538, 4356618, 7049156, 11405774, 18454930, 29860704, 48315634, 78176338, 126491972, 204668310, 331160282, 535828592, 866988874, 1402817466, 2269806340, 3672623806, 5942430146, 9615053952, 15557484098, more...

integer, monotonic, +

a(n)=a(n-1)+a(n-2)
a(0)=0
a(1)=2
n≥0
3 operations
Recursive
a(n)=lcm(a(n-1), 2)+a(n-2)
a(0)=0
a(1)=2
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility

Sequence 21tekj2nlzu5e

1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, more...

integer, periodic-6, non-monotonic, +-

a(n)=a(n-1)-a(n-2)
a(0)=1
a(1)=0
n≥0
3 operations
Recursive
a(n)=a(n-1)%2-a(n-2)
a(0)=1
a(1)=0
n≥0
5 operations
Divisibility
a(n)=a(n-1)^3-a(n-2)
a(0)=1
a(1)=0
n≥0
5 operations
Power
a(n)=round(sin(a(n-1)-a(n-2)))
a(0)=1
a(1)=0
n≥0
5 operations
Trigonometric

Sequence k4nocudelpwdn

1, 0, 1, -1, 2, -3, 5, -8, 13, -21, 34, -55, 89, -144, 233, -377, 610, -987, 1597, -2584, 4181, -6765, 10946, -17711, 28657, -46368, 75025, -121393, 196418, -317811, 514229, -832040, 1346269, -2178309, 3524578, -5702887, 9227465, -14930352, 24157817, -39088169, 63245986, -102334155, 165580141, -267914296, 433494437, -701408733, 1134903170, -1836311903, 2971215073, -4807526976, more...

integer, non-monotonic, +-

a(n)=a(n-2)-a(n-1)
a(0)=1
a(1)=0
n≥0
3 operations
Recursive

Sequence dexv1fek1b04f

1, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, 165580141, 267914296, 433494437, 701408733, 1134903170, 1836311903, 2971215073, 4807526976, more...

integer, non-monotonic, +, A212804

a(n)=a(n-1)+a(n-2)
a(0)=1
a(1)=0
n≥0
3 operations
Recursive

Sequence 0fhodl4yvailg

1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, more...

integer, periodic-6, non-monotonic, +-, A010892

a(n)=a(n-1)-a(n-2)
a(0)=1
a(1)=1
n≥0
3 operations
Recursive
a(n)=a(n-1)%2-a(n-2)
a(0)=1
a(1)=1
n≥0
5 operations
Divisibility
a(n)=a(n-1)^3-a(n-2)
a(0)=1
a(1)=1
n≥0
5 operations
Power
a(n)=round(sin(a(n-1)-a(n-2)))
a(0)=1
a(1)=1
n≥0
5 operations
Trigonometric

Sequence ntibcgspmesrd

1, 1, 0, 1, -1, 2, -3, 5, -8, 13, -21, 34, -55, 89, -144, 233, -377, 610, -987, 1597, -2584, 4181, -6765, 10946, -17711, 28657, -46368, 75025, -121393, 196418, -317811, 514229, -832040, 1346269, -2178309, 3524578, -5702887, 9227465, -14930352, 24157817, -39088169, 63245986, -102334155, 165580141, -267914296, 433494437, -701408733, 1134903170, -1836311903, 2971215073, more...

integer, non-monotonic, +-, A039834

a(n)=a(n-2)-a(n-1)
a(0)=1
a(1)=1
n≥0
3 operations
Recursive

Sequence wbrt3uagz3vqn

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, 165580141, 267914296, 433494437, 701408733, 1134903170, 1836311903, 2971215073, 4807526976, 7778742049, 12586269025, more...

integer, monotonic, +

a(n)=a(n-1)+a(n-2)
a(0)=1
a(1)=1
n≥0
3 operations
Recursive
a(n)=a(n-1)+a(n-2)%(2*a(n-2))
a(0)=1
a(1)=1
n≥0
7 operations
Divisibility

Sequence 5vanqp4ei4jlh

1, 1, 4, 27, 256, 3125, 46656, 823543, 16777216, 387420489, 10000000000, more...

integer, monotonic, +, A000312

a(n)=n^n
n≥0
3 operations
Power
a(n)=gcd(n, n!)^n
gcd(a,b)=greatest common divisor
n≥0
6 operations
Combinatoric
a(n)=n^(n%p(P(n)))
P(n)=Partition numbers
p(n)=nth prime
n≥0
7 operations
Prime

Sequence 3vpmrw5qzmkpc

1, 2, -1, 3, -4, 7, -11, 18, -29, 47, -76, 123, -199, 322, -521, 843, -1364, 2207, -3571, 5778, -9349, 15127, -24476, 39603, -64079, 103682, -167761, 271443, -439204, 710647, -1149851, 1860498, -3010349, 4870847, -7881196, 12752043, -20633239, 33385282, -54018521, 87403803, -141422324, 228826127, -370248451, 599074578, -969323029, 1568397607, -2537720636, 4106118243, -6643838879, 10749957122, more...

integer, non-monotonic, +-, A061084

a(n)=a(n-2)-a(n-1)
a(0)=1
a(1)=2
n≥0
3 operations
Recursive
a(n)=a(n-2)^(2-1)-a(n-1)
a(0)=1
a(1)=2
n≥0
7 operations
Power
a(n)=a(n-2)%(2*a(n-2))-a(n-1)
a(0)=1
a(1)=2
n≥0
7 operations
Divisibility

Sequence 4sc4axjz1i3ef

1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, more...

integer, periodic-6, non-monotonic, +-, A057079

a(n)=a(n-1)-a(n-2)
a(0)=1
a(1)=2
n≥0
3 operations
Recursive
a(n)=a(n-1)%3-a(n-2)
a(0)=1
a(1)=2
n≥0
5 operations
Divisibility
a(n)=a(n-1)^(2-1)-a(n-2)
a(0)=1
a(1)=2
n≥0
7 operations
Power

Sequence 5gu2v4kqgwlii

1, 2, 2, 1, 0.5, 0.5, 1, 2, 2, 1, 0.5, 0.5, 1, 2, 2, 1, 0.5, 0.5, 1, 2, 2, 1, 0.5, 0.5, 1, 2, 2, 1, 0.5, 0.5, 1, 2, 2, 1, 0.5, 0.5, 1, 2, 2, 1, 0.5, 0.5, 1, 2, 2, 1, 0.5, 0.5, 1, 2, more...

decimal, periodic-6, non-monotonic, +

a(n)=a(n-1)/a(n-2)
a(0)=1
a(1)=2
n≥0
3 operations
Recursive
a(n)=a(n-1)^(2-1)/a(n-2)
a(0)=1
a(1)=2
n≥0
7 operations
Power

Sequence q30xxumbskmcc

1, 2, 2, 4, 8, 32, 256, 8192, 2097152, 17179869184, more...

integer, monotonic, +, A000301

a(n)=a(n-1)*a(n-2)
a(0)=1
a(1)=2
n≥0
3 operations
Recursive
a(n)=lcm(a(n-1), 2)*a(n-2)
a(0)=1
a(1)=2
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility
a(n)=a(n-1)^(2-1)*a(n-2)
a(0)=1
a(1)=2
n≥0
7 operations
Power
a(n)=ϕ(2*a(n-2))*a(n-1)
a(0)=1
a(1)=2
ϕ(n)=number of relative primes (Euler's totient)
n≥0
6 operations
Prime

Sequence g14j5r0ijwyee

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, 165580141, 267914296, 433494437, 701408733, 1134903170, 1836311903, 2971215073, 4807526976, 7778742049, 12586269025, 20365011074, more...

integer, strictly-monotonic, +

a(n)=a(n-1)+a(n-2)
a(0)=1
a(1)=2
n≥0
3 operations
Recursive
a(n)=a(n-1)+a(n-2)%a(n-1)
a(0)=1
a(1)=2
n≥0
5 operations
Divisibility
a(n)=a(n-1)^(2-1)+a(n-2)
a(0)=1
a(1)=2
n≥0
7 operations
Power

Sequence 5mqgk4zvisdn

2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, more...

integer, periodic-6, non-monotonic, +-, A087204

a(n)=a(n-1)-a(n-2)
a(0)=2
a(1)=1
n≥0
3 operations
Recursive
a(n)=a(n-1)%3-a(n-2)
a(0)=2
a(1)=1
n≥0
5 operations
Divisibility

Sequence vkibyxn3uvpbi

2, 1, 0.5, 0.5, 1, 2, 2, 1, 0.5, 0.5, 1, 2, 2, 1, 0.5, 0.5, 1, 2, 2, 1, 0.5, 0.5, 1, 2, 2, 1, 0.5, 0.5, 1, 2, 2, 1, 0.5, 0.5, 1, 2, 2, 1, 0.5, 0.5, 1, 2, 2, 1, 0.5, 0.5, 1, 2, 2, 1, more...

decimal, periodic-6, non-monotonic, +

a(n)=a(n-1)/a(n-2)
a(0)=2
a(1)=1
n≥0
3 operations
Recursive

Sequence b3nzmx3ifjtfh

2, 1, 1, 0, 1, -1, 2, -3, 5, -8, 13, -21, 34, -55, 89, -144, 233, -377, 610, -987, 1597, -2584, 4181, -6765, 10946, -17711, 28657, -46368, 75025, -121393, 196418, -317811, 514229, -832040, 1346269, -2178309, 3524578, -5702887, 9227465, -14930352, 24157817, -39088169, 63245986, -102334155, 165580141, -267914296, 433494437, -701408733, 1134903170, -1836311903, more...

integer, non-monotonic, +-

a(n)=a(n-2)-a(n-1)
a(0)=2
a(1)=1
n≥0
3 operations
Recursive

Sequence avhxlllntzhjc

2, 1, 2, 2, 4, 8, 32, 256, 8192, 2097152, 17179869184, more...

integer, non-monotonic, +

a(n)=a(n-1)*a(n-2)
a(0)=2
a(1)=1
n≥0
3 operations
Recursive
a(n)=lcm(a(n-1)*a(n-2), 2)
a(0)=2
a(1)=1
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility

Sequence 2ey5bsf5kxnzc

2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, 15127, 24476, 39603, 64079, 103682, 167761, 271443, 439204, 710647, 1149851, 1860498, 3010349, 4870847, 7881196, 12752043, 20633239, 33385282, 54018521, 87403803, 141422324, 228826127, 370248451, 599074578, 969323029, 1568397607, 2537720636, 4106118243, 6643838879, 10749957122, 17393796001, more...

integer, non-monotonic, +, A000032

a(n)=a(n-1)+a(n-2)
a(0)=2
a(1)=1
n≥0
3 operations
Recursive

Sequence e0jbbhm1njb1f

2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, more...

integer, periodic-6, non-monotonic, +-, A130772

a(n)=a(n-1)-a(n-2)
a(0)=2
a(1)=2
n≥0
3 operations
Recursive
a(n)=a(n-1)%3-a(n-2)
a(0)=2
a(1)=2
n≥0
5 operations
Divisibility
a(n)=round(a(n-1)+tan(a(n-2)))
a(0)=2
a(1)=2
n≥0
5 operations
Trigonometric

Sequence ejvfgqmkzvs0p

2, 2, 0, 2, -2, 4, -6, 10, -16, 26, -42, 68, -110, 178, -288, 466, -754, 1220, -1974, 3194, -5168, 8362, -13530, 21892, -35422, 57314, -92736, 150050, -242786, 392836, -635622, 1028458, -1664080, 2692538, -4356618, 7049156, -11405774, 18454930, -29860704, 48315634, -78176338, 126491972, -204668310, 331160282, -535828592, 866988874, -1402817466, 2269806340, -3672623806, 5942430146, more...

integer, non-monotonic, +-

a(n)=a(n-2)-a(n-1)
a(0)=2
a(1)=2
n≥0
3 operations
Recursive

Sequence tajomw0vtodfb

2, 2, 1, 0.5, 0.5, 1, 2, 2, 1, 0.5, 0.5, 1, 2, 2, 1, 0.5, 0.5, 1, 2, 2, 1, 0.5, 0.5, 1, 2, 2, 1, 0.5, 0.5, 1, 2, 2, 1, 0.5, 0.5, 1, 2, 2, 1, 0.5, 0.5, 1, 2, 2, 1, 0.5, 0.5, 1, 2, 2, more...

decimal, periodic-6, non-monotonic, +

a(n)=a(n-1)/a(n-2)
a(0)=2
a(1)=2
n≥0
3 operations
Recursive

Sequence robde2zb4suge

2, 2, 4, 6, 10, 16, 26, 42, 68, 110, 178, 288, 466, 754, 1220, 1974, 3194, 5168, 8362, 13530, 21892, 35422, 57314, 92736, 150050, 242786, 392836, 635622, 1028458, 1664080, 2692538, 4356618, 7049156, 11405774, 18454930, 29860704, 48315634, 78176338, 126491972, 204668310, 331160282, 535828592, 866988874, 1402817466, 2269806340, 3672623806, 5942430146, 9615053952, 15557484098, 25172538050, more...

integer, monotonic, +

a(n)=a(n-1)+a(n-2)
a(0)=2
a(1)=2
n≥0
3 operations
Recursive
a(n)=lcm(a(n-1), 2)+a(n-2)
a(0)=2
a(1)=2
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility

Sequence refctlmyg0ilc

2, 2, 4, 8, 32, 256, 8192, 2097152, 17179869184, more...

integer, monotonic, +

a(n)=a(n-1)*a(n-2)
a(0)=2
a(1)=2
n≥0
3 operations
Recursive
a(n)=lcm(a(n-1), 2)*a(n-2)
a(0)=2
a(1)=2
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility
a(n)=a(n-1)*a(n-2)%(a(n-2)^2)
a(0)=2
a(1)=2
n≥0
7 operations
Power

Sequence ukjrtzwdrsstc

2, 3, -1, 4, -5, 9, -14, 23, -37, 60, -97, 157, -254, 411, -665, 1076, -1741, 2817, -4558, 7375, -11933, 19308, -31241, 50549, -81790, 132339, -214129, 346468, -560597, 907065, -1467662, 2374727, -3842389, 6217116, -10059505, 16276621, -26336126, 42612747, -68948873, 111561620, -180510493, 292072113, -472582606, 764654719, -1237237325, 2001892044, -3239129369, 5241021413, -8480150782, 13721172195, more...

integer, non-monotonic, +-

a(n)=a(n-2)-a(n-1)
a(0)=2
a(1)=3
n≥0
3 operations
Recursive
a(n)=a(n-2)%(2*a(n-2))-a(n-1)
a(0)=2
a(1)=3
n≥0
7 operations
Divisibility

Sequence ljlutso4hbofj

2, 3, 1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, more...

integer, periodic-6, non-monotonic, +-

a(n)=a(n-1)-a(n-2)
a(0)=2
a(1)=3
n≥0
3 operations
Recursive
a(n)=a(n-1)%4-a(n-2)
a(0)=2
a(1)=3
n≥0
5 operations
Divisibility
a(n)=a(n-1)^2/a(n-1)-a(n-2)
a(0)=2
a(1)=3
n≥0
7 operations
Power

Sequence 40y3tglbjg4pg

2, 3, 1.5, 0.5, 0.3333333333, 0.6666666667, 2, 3, 1.5, 0.5, 0.3333333333, 0.6666666667, 2, 3, 1.5, 0.5, 0.3333333333, 0.6666666667, 2, 3, 1.5, 0.5, 0.3333333333, 0.6666666667, 2, 3, 1.5, 0.5, 0.3333333333, 0.6666666667, 2, 3, 1.5, 0.5, 0.3333333333, 0.6666666667, 2, 3, 1.5, 0.5, 0.3333333333, 0.6666666667, 2, 3, 1.5, 0.5, 0.3333333333, 0.6666666667, 2, 3, more...

decimal, periodic-6, non-monotonic, +

a(n)=a(n-1)/a(n-2)
a(0)=2
a(1)=3
n≥0
3 operations
Recursive

Sequence 5exrdiuxaczsd

2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, 165580141, 267914296, 433494437, 701408733, 1134903170, 1836311903, 2971215073, 4807526976, 7778742049, 12586269025, 20365011074, 32951280099, more...

integer, strictly-monotonic, +, A020695

a(n)=a(n-1)+a(n-2)
a(0)=2
a(1)=3
n≥0
3 operations
Recursive
a(n)=a(n-1)+a(n-2)%a(n-1)
a(0)=2
a(1)=3
n≥0
5 operations
Divisibility

Sequence vvuphvknunk5d

2, 3, 6, 18, 108, 1944, 209952, 408146688, more...

integer, strictly-monotonic, +, A000304

a(n)=a(n-1)*a(n-2)
a(0)=2
a(1)=3
n≥0
3 operations
Recursive
a(n)=lcm(a(n-1), 3)*a(n-2)
a(0)=2
a(1)=3
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility
a(n)=a(n-1)%(a(n-1)^2)*a(n-2)
a(0)=2
a(1)=3
n≥0
7 operations
Power

Sequence lpylbs2ffxw3k

3, 9, 81, 6561, 43046721, more...

integer, strictly-monotonic, +, A011764

a(n)=a(n-1)*a(n-1)
a(0)=3
n≥0
3 operations
Recursive
a(n)=a(n-1)^2
a(0)=3
n≥0
3 operations
Power
a(n)=lcm(a(n-1), 3)*a(n-1)
a(0)=3
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility
a(n)=3^τ(n!)
τ(n)=number of divisors of n
n≥1
5 operations
Prime

Sequence vusq2s4v30qyc

4, 16, 256, 65536, 4294967296, more...

integer, strictly-monotonic, +

a(n)=a(n-1)*a(n-1)
a(0)=4
n≥0
3 operations
Recursive
a(n)=a(n-1)^2
a(0)=4
n≥0
3 operations
Power
a(n)=lcm(a(n-1), 2)*a(n-1)
a(0)=4
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility
a(n)=4^τ(n!)
τ(n)=number of divisors of n
n≥1
5 operations
Prime

Sequence xeqru1sygmtfp

0, 0.6931471806, 1.0986122887, 0.6931471806, 1.6094379124, 0, 1.9459101491, 0.6931471806, 1.0986122887, 0, 2.3978952728, 0, 2.5649493575, 0, 0, 0.6931471806, 2.8332133441, 0, 2.9444389792, 0, 0, 0, 3.1354942159, 0, 1.6094379124, 0, 1.0986122887, 0, 3.36729583, 0, 3.4339872045, 0.6931471806, 0, 0, 0, 0, 3.6109179126, 0, 0, 0, 3.7135720667, 0, 3.7612001157, 0, 0, 0, 3.8501476017, 0, 1.9459101491, 0, more...

decimal, non-monotonic, +

a(n)=Λ(n)
Λ(n)=Von Mangoldt's function
n≥1
2 operations
Prime

Sequence 1geoyb5xzuhhk

0, 1, 0.5403023059, 0.8575532158, 0.6542897905, 0.7934803587, 0.7013687736, 0.7639596829, 0.722102425, 0.7504177618, 0.7314040424, 0.7442373549, 0.7356047404, 0.7414250866, 0.7375068905, 0.7401473356, 0.7383692041, 0.7395672022, 0.7387603199, 0.7393038924, 0.7389377567, 0.7391843998, 0.7390182624, 0.7391301765, 0.7390547907, 0.7391055719, 0.7390713653, 0.7390944074, 0.739078886, 0.7390893414, 0.7390822985, 0.7390870427, 0.739083847, 0.7390859996, 0.7390845496, 0.7390855264, 0.7390848684, 0.7390853116, 0.739085013, 0.7390852142, 0.7390850787, 0.7390851699, 0.7390851085, 0.7390851499, 0.739085122, 0.7390851408, 0.7390851281, 0.7390851366, 0.7390851309, 0.7390851348, more...

decimal, non-monotonic, +

a(n)=cos(a(n-1))
a(0)=0
n≥0
2 operations
Trigonometric
a(n)=cos(λ(n)*a(n-1))
a(0)=0
λ(n)=Liouville's function
n≥0
5 operations
Prime

Sequence ub3tktmvdthvj

0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 4, 1, 3, 1, 3, 2, 2, 1, 4, 2, 2, 3, 3, 1, 3, 1, 5, 2, 2, 2, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 1, 5, 2, 3, more...

integer, non-monotonic, +, A001222

a(n)=Ω(n)
Ω(n)=max factorization terms
n≥1
2 operations
Prime

Sequence 3bmepyefoqlfp

1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, -1, 0, 1, 1, -1, 0, 0, 1, 0, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, 1, 1, 0, -1, -1, -1, 0, 0, 1, -1, 0, 0, 0, more...

integer, non-monotonic, +-, A008683

a(n)=μ(n)
μ(n)=Möbius function
n≥1
2 operations
Prime

Sequence 5as1ecrpxvlwn

1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, more...

integer, non-monotonic, +-, A008836

a(n)=λ(n)
λ(n)=Liouville's function
n≥1
2 operations
Prime

Sequence ah3e125oj0u1p

1, 0.5403023059, 0.8575532158, 0.6542897905, 0.7934803587, 0.7013687736, 0.7639596829, 0.722102425, 0.7504177618, 0.7314040424, 0.7442373549, 0.7356047404, 0.7414250866, 0.7375068905, 0.7401473356, 0.7383692041, 0.7395672022, 0.7387603199, 0.7393038924, 0.7389377567, 0.7391843998, 0.7390182624, 0.7391301765, 0.7390547907, 0.7391055719, 0.7390713653, 0.7390944074, 0.739078886, 0.7390893414, 0.7390822985, 0.7390870427, 0.739083847, 0.7390859996, 0.7390845496, 0.7390855264, 0.7390848684, 0.7390853116, 0.739085013, 0.7390852142, 0.7390850787, 0.7390851699, 0.7390851085, 0.7390851499, 0.739085122, 0.7390851408, 0.7390851281, 0.7390851366, 0.7390851309, 0.7390851348, 0.7390851322, more...

decimal, non-monotonic, +

a(n)=cos(a(n-1))
a(0)=1
n≥0
2 operations
Trigonometric
a(n)=cos(λ(n)*a(n-1))
a(0)=1
λ(n)=Liouville's function
n≥0
5 operations
Prime

Sequence 3vjrf4syydoyh

1, 0.8414709848, 0.7456241417, 0.6784304774, 0.627571832, 0.5871809966, 0.5540163908, 0.5261070755, 0.5021706763, 0.4813293553, 0.4629578985, 0.4465965934, 0.4318984333, 0.418595661, 0.406477765, 0.395376547, 0.3851557131, 0.3757034468, 0.3669270011, 0.3587486881, 0.351102859, 0.3439335943, 0.3371929169, 0.3308393911, 0.3248370136, 0.3191543275, 0.3137637059, 0.3086407708, 0.3037639155, 0.2991139106, 0.2946735773, 0.2904275127, 0.2863618603, 0.2824641153, 0.2787229586, 0.275128116, 0.2716702368, 0.2683407895, 0.2651319715, 0.2620366305, 0.2590481967, 0.2561606224, 0.2533683302, 0.2506661666, 0.2480493614, 0.2455134918, 0.2430544503, 0.2406684166, 0.2383518317, 0.2361013758, more...

decimal, strictly-monotonic, +

a(n)=sin(a(n-1))
a(0)=1
n≥0
2 operations
Trigonometric

Sequence 2q1rtmulmg2m

1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, 12, 6, 8, 8, 16, 6, 18, 8, 12, 10, 22, 8, 20, 12, 18, 12, 28, 8, 30, 16, 20, 16, 24, 12, 36, 18, 24, 16, 40, 12, 42, 20, 24, 22, 46, 16, 42, 20, more...

integer, non-monotonic, +, A000010

a(n)=ϕ(n)
ϕ(n)=number of relative primes (Euler's totient)
n≥1
2 operations
Prime

Sequence rr0pwa4zvo2oh

1, 1.5574077247, 74.6859333988, -0.8635188549, -1.1698563551, -2.3590377342, 0.994329619, 1.5381535569, 30.623773508, -1.0136018143, -1.6050123678, 29.2146517707, 1.3701487455, 4.9167999905, -4.8237768261, 8.9404801577, -0.5260857889, -0.580671062, -0.6561279832, -0.7699191877, -0.9695115437, -1.4576737055, -8.8022251344, 0.7177699669, 0.8731301134, 1.1928808263, 2.5189063581, -0.7179722179, -0.8734866146, -1.1937449837, -2.525267346, 0.7083759388, 0.8567086986, 1.1538533121, 2.2577904353, -1.2190733997, -2.7249276145, 0.4425784376, 0.4739342704, 0.5129252615, 0.5632055447, 0.6314240774, 0.7312981266, 0.8972580163, 1.2530863851, 3.0409021585, -0.1010321668, -0.1013773381, -0.1017260691, -0.1020784213, more...

decimal, non-monotonic, +-

a(n)=tan(a(n-1))
a(0)=1
n≥0
2 operations
Trigonometric