Sequence Database

A database with 1693109 machine generated integer and decimal sequences.

Displaying result 0-99 of total 1477560. [0] [1] [2] [3] [4] ... [14775]

Sequence rqze1ag3ydclb

0, 0.6931471805599453, 1.0986122886681098, 0.6931471805599453, 1.6094379124341003, 0, 1.9459101490553132, 0.6931471805599453, 1.0986122886681098, 0, 2.3978952727983707, 0, 2.5649493574615367, 0, 0, 0.6931471805599453, 2.833213344056216, 0, 2.9444389791664403, 0, 0, 0, 3.1354942159291497, 0, 1.6094379124341003, more...

decimal, non-monotonic, +

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

Sequence 3nnc4n44b0b5n

0, 0.6931471805599453, 1.0986122886681098, 1.3862943611198906, 1.6094379124341003, 1.791759469228055, 1.9459101490553132, 2.0794415416798357, 2.1972245773362196, 2.302585092994046, 2.3978952727983707, 2.4849066497880004, 2.5649493574615367, 2.6390573296152584, 2.70805020110221, 2.772588722239781, 2.833213344056216, 2.8903717578961645, 2.9444389791664403, 2.995732273553991, 3.044522437723423, 3.091042453358316, 3.1354942159291497, 3.1780538303479458, 3.2188758248682006, more...

decimal, strictly-monotonic, +

a(n)=log(n)
n≥1
2 operations
Power

Sequence pv1sq0qzw5fdm

0, 0.7615941559557649, 0.9640275800758169, 0.9950547536867305, 0.999329299739067, 0.9999092042625951, 0.9999877116507956, 0.9999983369439447, 0.9999997749296758, 0.999999969540041, 0.9999999958776927, 0.9999999994421064, 0.9999999999244973, 0.9999999999897818, 0.9999999999986171, 0.9999999999998128, 0.9999999999999747, 1, 1, 1, 1, 1, 1, 1, 1, more...

decimal, monotonic, +

a(n)=tanh(n)
n≥0
2 operations
Trigonometric
a(n)=sin(atan(sinh(n)))
n≥0
4 operations
Trigonometric

Sequence daf0zbaa4ck0j

0, 0.7853981633974483, 1.1071487177940904, 1.2490457723982544, 1.3258176636680326, 1.373400766945016, 1.4056476493802699, 1.4288992721907328, 1.446441332248135, 1.460139105621001, 1.4711276743037347, 1.4801364395941514, 1.4876550949064553, 1.4940244355251187, 1.4994888620096063, 1.5042281630190728, 1.5083775167989393, 1.512040504079174, 1.5152978215491797, 1.5182132651839548, 1.5208379310729538, 1.5232132235179132, 1.5253730473733196, 1.5273454314033659, 1.5291537476963082, more...

decimal, strictly-monotonic, +

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

Sequence lcv1zgpjttqpl

0, 0.8414709848078965, 0.9092974268256817, 0.1411200080598672, -0.7568024953079282, -0.9589242746631385, -0.27941549819892586, 0.6569865987187891, 0.9893582466233818, 0.4121184852417566, -0.5440211108893698, -0.9999902065507035, -0.5365729180004349, 0.4201670368266409, 0.9906073556948704, 0.6502878401571168, -0.2879033166650653, -0.9613974918795568, -0.7509872467716762, 0.14987720966295234, 0.9129452507276277, 0.8366556385360561, -0.008851309290403876, -0.8462204041751706, -0.9055783620066238, more...

decimal, non-monotonic, +-

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

Sequence ccgud0zu4fvbp

0, 1, 0.5403023058681398, 0.8575532158463934, 0.6542897904977791, 0.7934803587425656, 0.7013687736227565, 0.7639596829006542, 0.7221024250267077, 0.7504177617637605, 0.7314040424225098, 0.7442373549005569, 0.7356047404363474, 0.7414250866101092, 0.7375068905132428, 0.7401473355678757, 0.7383692041223232, 0.7395672022122561, 0.7387603198742113, 0.7393038923969059, 0.7389377567153445, 0.7391843997714936, 0.7390182624274122, 0.7391301765296711, 0.7390547907469174, more...

decimal, non-monotonic, convergent, +

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

Sequence ncilpddnshefo

0, 1, 1, 1, 16, 2, 2, 2, 2, 1, 18, 2, 2, 11, 1, 1, 2, 4, 1, 16, 3, 2, 4, 21, 2, 405, 2, 1, 33, 1, 2, 8, 2, 29, 1, 4, 4, 4, 4, 1, 9, 3, 1, 4, 1, 1, 2, 26, 1, 8, more...

integer, non-monotonic, +, A065645

a(n)=contfrac[TwinPrime]
TwinPrime=0.6601... (Twin Prime)
contfrac(a)=continued fraction of a
n≥0
2 operations
DecimalConstant

Sequence brsi1x4psomni

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 distinct factors of n
n≥1
2 operations
Prime
a(n)=log(sqrt(exp(Ω(n²))))
Ω(n)=max distinct factors of n
n≥1
6 operations
Prime
a(n)=Ω(n*p(n))-1
p(n)=nth prime
Ω(n)=max distinct factors of n
n≥1
7 operations
Prime

Sequence 2co2c3vr2pedl

0, 1, 1, 2, 1, 2, 1, 4, 3, 13, 5, 1, 1, 8, 1, 2, 4, 1, 1, 40, 1, 11, 3, 7, 1, 7, 1, 1, 5, 1, 49, 4, 1, 65, 1, 4, 7, 11, 1, 399, 2, 1, 3, 2, 1, 2, 1, 5, 3, 2, more...

integer, non-monotonic, +, A002852

a(n)=contfrac[γ]
γ=0.5772... (Euler Gamma)
contfrac(a)=continued fraction of a
n≥0
2 operations
DecimalConstant

Sequence f0hiz4pasazlk

0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 6, 5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 2, 9, more...

integer, non-monotonic, +, A002487

a(n)=stern(n)
stern(n)=Stern-Brocot sequence
n≥0
2 operations
Recursive

Sequence g3fycrmfjmnxl

0, 1, 1, 3, 4, 2, 10, 4, 1, 1, 1, 1, 2, 7, 306, 1, 5, 1, 2, 1, 5, 1, 1, 1, 1, 7, 1, 4, 2, 15, 1, 2, 1, 1, 4, 1, 3, 3, 5, 4, 1, 1, 1, 4, 3, 1, 38, 1, 2, 4, more...

integer, non-monotonic, +, A019474

a(n)=contfrac[W1]
W1=0.5671... (Lambert W)
contfrac(a)=continued fraction of a
n≥0
2 operations
DecimalConstant
a(n)=contfrac[log(W1)]
W1=0.5671... (Lambert W)
contfrac(a)=continued fraction of a
n≥0
3 operations
Power

Sequence pbxjymlmanmwo

0, 1, 1.4142135623730951, 1.7320508075688772, 2, 2.23606797749979, 2.449489742783178, 2.6457513110645907, 2.8284271247461903, 3, 3.1622776601683795, 3.3166247903554, 3.4641016151377544, 3.605551275463989, 3.7416573867739413, 3.872983346207417, 4, 4.123105625617661, 4.242640687119285, 4.358898943540674, 4.47213595499958, 4.58257569495584, 4.69041575982343, 4.795831523312719, 4.898979485566356, more...

decimal, strictly-monotonic, +

a(n)=sqrt(n)
n≥0
2 operations
Power

Sequence h2nzadzb4rcpj

0, 1, 1.5849625007211563, 2, 2.321928094887362, 2.584962500721156, 2.807354922057604, 3, 3.1699250014423126, 3.3219280948873626, 3.4594316186372978, 3.5849625007211565, 3.700439718141092, 3.8073549220576037, 3.9068905956085187, 4, 4.08746284125034, 4.169925001442312, 4.247927513443585, 4.321928094887363, 4.392317422778761, 4.459431618637297, 4.523561956057013, 4.584962500721157, 4.643856189774724, more...

decimal, strictly-monotonic, +

a(n)=log2(n)
n≥1
2 operations
Power

Sequence 5ey1pvojvkhlg

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)=partial sums of a
n≥0
2 operations
Variable
a(n)=n+a(n-1)
a(0)=0
n≥0
3 operations
Recursive
a(n)=-∑[-n]
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=∑[C(n, a(n-1))]
a(0)=0
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=∑[and(n, -1)]
and(a,b)=bitwise and
∑(a)=partial sums of a
n≥0
5 operations
Bitwise

Sequence hr1xwu5kzwtrb

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)=n²
n≥0
2 operations
Power
a(n)=Δ[n²]+a(n-1)
a(0)=0
Δ(a)=differences of a
n≥0
5 operations
Recursive
a(n)=C(n, sqrt(a(n-1)))²
a(0)=0
C(n,k)=binomial coefficient
n≥0
5 operations
Combinatoric
a(n)=∑[2*n]-n
∑(a)=partial sums of a
n≥0
6 operations
Arithmetic
a(n)=∑[or(1, 1+a(n-1))]
a(0)=0
or(a,b)=bitwise or
∑(a)=partial sums of a
n≥0
6 operations
Recursive

Sequence 2e2pf0fazbckl

0, 1, 10, 1, 8, 1, 88, 4, 1, 1, 7, 22, 1, 2, 3, 26, 1, 11, 1, 10, 1, 9, 3, 1, 1, 1, 1, 1, 1, 2, 2, 1, 11, 1, 1, 1, 6, 1, 12, 1, 4, 7, 1, 1, 2, 5, 1, 5, 9, 1, more...

integer, non-monotonic, +, A014538

a(n)=contfrac[G]
G=0.9159... (Catalans)
contfrac(a)=continued fraction of a
n≥0
2 operations
DecimalConstant

Sequence o32blh3uvkhdm

0, 1.1752011936438014, 3.626860407847019, 10.017874927409903, 27.28991719712775, 74.20321057778875, 201.71315737027922, 548.3161232732465, 1490.4788257895502, 4051.54190208279, 11013.232874703393, 29937.07084924806, 81377.39570642984, 221206.6960033301, 601302.1420819727, 1634508.6862359024, 4443055.26025388, 12077476.376787629, 32829984.568665247, 89241150.48159364, 242582597.70489514, 659407867.2416073, 1792456423.065796, 4872401723.124452, 13244561064.921736, more...

decimal, strictly-monotonic, +

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

Sequence tggbolmv0svvn

0, 1.5574077246549023, -2.185039863261519, -0.1425465430742778, 1.1578212823495777, -3.380515006246586, -0.29100619138474915, 0.8714479827243187, -6.799711455220379, -0.45231565944180985, 0.6483608274590866, -225.95084645419513, -0.6358599286615808, 0.4630211329364896, 7.2446066160948055, -0.8559934009085188, 0.3006322420239034, 3.49391564547484, -1.1373137123376869, 0.15158947061240008, 2.237160944224742, -1.5274985276366035, 0.00885165604168446, 1.5881530833912738, -2.1348966977217008, more...

decimal, non-monotonic, +-

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

Sequence g4ygqqbyryufl

0, 1.5707963267948966, 0.5669115049410094, 1.0550620112573421, 0.7586112145937554, 0.9218067818082122, 0.8260630799508202, 0.880364061711098, 0.8489363384272013, 0.8669200971125083, 0.856560920825803, 0.8625056203158679, 0.8590867594493288, 0.861050527953115, 0.8599217423241453, 0.860570307066057, 0.8601975736780776, 0.8604117562009795, 0.8602886715766134, 0.860359401635384, 0.860318755854242, 0.8603421130376111, 0.8603286906684817, 0.8603364038890915, 0.8603319714420676, more...

decimal, non-monotonic, convergent, +

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

Sequence jsxfs42lrpw3p

0, 2, 1, 2, 14, 1, 1, 2, 3, 5, 1, 3, 1, 5, 1, 1, 2, 3, 5, 46, 2, 2, 4, 4, 2, 1, 6, 1, 1, 4, 2, 2, 1, 109, 1, 1, 4, 9, 3, 45, 8, 4, 1, 2, 1, 13, 13, 1, 1, 2, more...

integer, non-monotonic, +, A048296

a(n)=contfrac[Artins]
Artins=0.3739... (Artins)
contfrac(a)=continued fraction of a
n≥0
2 operations
DecimalConstant

Sequence ebfmjj0402bb

0, 2, 1, 14, 1, 3, 8, 1, 5, 2, 7, 1, 12, 1, 5, 59, 1, 1, 1, 3, 1, 3, 1, 36, 2, 1, 1, 1, 5, 1, 5, 2, 3, 1, 2, 1, 255, 1, 1, 26, 4, 5, 1, 5, 1, 2, 1, 3, 5, 1, more...

integer, non-monotonic, +

a(n)=contfrac[Pólya_D3]
Pólya_D3=0.3405... (Pólya random walk 3D)
contfrac(a)=continued fraction of a
n≥0
2 operations
DecimalConstant

Sequence kusc5pibufhkj

0, 3, 1, 4, 1, 2, 5, 2, 1, 1, 1, 1, 13, 4, 2, 4, 2, 1, 33, 296, 2, 1, 5, 19, 1, 5, 1, 1, 1, 1, 1, 12, 12, 9, 1, 8, 4, 10, 2, 1, 1, 3, 1, 1, 1, 1, 2, 2, 2, 1, more...

integer, non-monotonic, +, A230767

a(n)=contfrac[Mertens]
Mertens=0.2614... (Mertens)
contfrac(a)=continued fraction of a
n≥0
2 operations
DecimalConstant

Sequence 4cpzl0cv2iyxp

0, 4, 4, 8, 16, 18, 5, 1, 1, 1, 1, 7, 1, 1, 6, 2, 9, 58, 1, 3, 4, 2, 2, 1, 1, 2, 1, 4, 39, 4, 4, 5, 2, 1, 1, 87, 16, 1, 2, 1, 2, 1, 1, 3, 1, 8, 1, 3, 1, 1, more...

integer, non-monotonic, +, A030168

a(n)=contfrac[CopelandErdős]
CopelandErdős=0.2357... (Copeland-Erdős)
contfrac(a)=continued fraction of a
n≥0
2 operations
DecimalConstant

Sequence t1zgct2gyon3m

0, 7, 2, 8, 1, 5, 8, 4, 5, 4, 8, 3, 6, 7, 6, 7, 2, 4, 8, 6, 0, 5, 8, 6, 3, 7, 5, 8, 7, 4, 9, 0, 1, 3, 1, 9, 1, 3, 7, 7, 3, 6, 3, 3, 8, 3, 3, 4, 3, 3, more...

integer, non-monotonic, +, A082633

a(n)=de[Stieltjes]
Stieltjes=0.0728... (Stieltjes gamma(1))
de(a)=decimal expansion of a
n≥0
2 operations
DecimalConstant

Sequence ruhaqit5bcw0k

0, 13, 1, 2, 1, 2, 1, 74, 1, 10, 1, 9, 2, 1, 3, 1, 4, 1, 6, 1, 1, 2, 84, 1, 108, 1, 20, 22, 2, 2, 1, 2, 2, 1, 7, 1, 66, 2, 1, 1, 2, 5, 1, 1, 2, 1, 1, 59, 1, 2, more...

integer, non-monotonic, +, A066036

a(n)=contfrac[Stieltjes]
Stieltjes=0.0728... (Stieltjes gamma(1))
contfrac(a)=continued fraction of a
n≥0
2 operations
DecimalConstant

Sequence jf1vodtk3fpuj

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 sxgqtfmeezvbp

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
a(n)=(-1)^Ω(n)
Ω(n)=max distinct factors of n
n≥1
5 operations
Prime
a(n)=μ(or(6, Ω(n)))
Ω(n)=max distinct factors of n
or(a,b)=bitwise or
μ(n)=Möbius function
n≥1
5 operations
Prime

Sequence tdb3tixo3q50e

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

Sequence 2mcooaevb1qke

1, 0.5403023058681398, -0.4161468365471424, -0.9899924966004454, -0.6536436208636119, 0.28366218546322625, 0.9601702866503661, 0.7539022543433046, -0.14550003380861354, -0.9111302618846769, -0.8390715290764524, 0.004425697988050785, 0.8438539587324921, 0.9074467814501962, 0.1367372182078336, -0.7596879128588213, -0.9576594803233847, -0.27516333805159693, 0.6603167082440802, 0.9887046181866692, 0.40808206181339196, -0.5477292602242684, -0.9999608263946371, -0.5328330203333975, 0.424179007336997, more...

decimal, non-monotonic, +-

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

Sequence pl1msqvbe0jxf

1, 0.5403023058681398, 0.8575532158463934, 0.6542897904977791, 0.7934803587425656, 0.7013687736227565, 0.7639596829006542, 0.7221024250267077, 0.7504177617637605, 0.7314040424225098, 0.7442373549005569, 0.7356047404363474, 0.7414250866101092, 0.7375068905132428, 0.7401473355678757, 0.7383692041223232, 0.7395672022122561, 0.7387603198742113, 0.7393038923969059, 0.7389377567153445, 0.7391843997714936, 0.7390182624274122, 0.7391301765296711, 0.7390547907469174, 0.7391055719265363, more...

decimal, non-monotonic, +

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

Sequence mko4mgfp3pynf

1, 0.6420926159343308, 1.3372531775192829, 0.23788387690605642, 4.12413633154056, 0.6670279034307094, 1.2699574736317798, 0.3102556105005124, 3.1190604630027807, -44.37343795786241, -2.4248943131588243, 1.1477850226460427, 0.4501892604691449, 2.069157407113594, -0.5441763422005822, -1.6525623988614118, 0.08194878158265755, 12.175415468226646, -2.4261722603240066, 1.1507509027647633, 0.44662703019981215, 2.088110796239434, -0.5690013762475906, -1.5635736046906987, -0.007222847704453914, more...

decimal, non-monotonic, +-

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

Sequence t4sai1a5ixxrb

1, 0.7615941559557649, 0.6420149920119997, 0.5662699759614798, 0.5126146671514058, 0.47197991599628375, 0.4397976612426585, 0.4134767099038357, 0.39142072274619333, 0.37258437431195934, 0.35625016733262493, 0.3419068135829597, 0.32917865455566736, 0.31778256849828124, 0.30750053381285786, 0.2981615348459582, 0.28962926538567413, 0.28179355287091506, 0.2745642407809474, 0.2678667368891988, 0.26163871605273287, 0.2558276392816409, 0.2503888603364445, 0.24528416206577766, 0.24048061168636833, more...

decimal, strictly-monotonic, convergent, +

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

Sequence fjqeqjkdd5hzl

1, 0.7853981633974483, 0.6657737500283538, 0.5873841757054615, 0.5310915101557615, 0.48821033776057654, 0.4541714733496343, 0.42631750614498276, 0.4029860575289656, 0.3830779111188442, 0.3658337988552085, 0.3507104328555913, 0.3373075814566938, 0.3253231030321183, 0.31452410696550526, 0.3047278305397643, 0.29578858986287454, 0.28758865114386256, 0.2800317035979962, 0.2730381015817184, 0.2665413362510722, 0.26048537837265157, 0.25482264919640507, 0.24951245130128574, 0.24451974114927352, more...

decimal, strictly-monotonic, convergent, +

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

Sequence ujc35vfizaa1h

1, 0.7853981633974483, 0.9050225767665427, 0.8352132406069623, 0.8749496223708837, 0.8519948603481292, 0.8651452827866869, 0.8575750932355533, 0.8619209364833037, 0.8594221270660236, 0.8608576014691751, 0.8600325405331767, 0.8605066138531038, 0.8602341679011974, 0.8603907246919031, 0.8603007566345732, 0.8603524566268336, 0.8603227467514742, 0.8603398196185867, 0.8603300085840736, 0.8603356465388472, 0.8603324066562877, 0.8603342684708953, 0.8603331985691531, 0.8603338133936824, more...

decimal, non-monotonic, +

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

Sequence cos52tc5kvjs

1, 0.8414709848078965, 0.7456241416655579, 0.6784304773607402, 0.6275718320491591, 0.5871809965734309, 0.5540163907556296, 0.5261070755028416, 0.5021706762685553, 0.48132935526234627, 0.46295789853781183, 0.44659659338698193, 0.43189843326582245, 0.41859566099821055, 0.4064777649840687, 0.39537654698883457, 0.38515571309652635, 0.3757034468477152, 0.3669270010627914, 0.3587486881078098, 0.35110285896317867, 0.3439335943286482, 0.33719291693600184, 0.3308393910703576, 0.32483701364027, more...

decimal, strictly-monotonic, convergent, +

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

Sequence lalqvjgjzo0ro

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

Sequence t2oz3rjao0lvj

1, 1, 1, 1, 21, 1, 1, 1, 6, 4, 2, 1, 1, 2, 1, 3, 1, 13, 13, 6, 1, 5, 2, 1, 15, 1, 12, 1, 1, 1, 8, 13, 4, 1, 1, 1, 1, 1, 1, 15, 1, 1, 1, 1, 1, 1, 2, 1, 4, 1, more...

integer, non-monotonic, +

a(n)=contfrac[QR]
QR=1.6616... (Quadratic Recurrence)
contfrac(a)=continued fraction of a
n≥0
2 operations
DecimalConstant

Sequence pvurlm0y53im

1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 5, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 3, 2, 1, 1, 1, 7, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 5, 2, 2, more...

integer, non-monotonic, +, A000688

a(n)=agc(n)
agc(n)=number of factorizations into prime powers (abelian group count)
n≥0
2 operations
Prime

Sequence gv5wnaqfuuoao

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 dps4an1f0bv5f

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

Sequence jlpqc0m0fwl2i

1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304, more...

integer, monotonic, +, A000108

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

Sequence fgxbahcl0w5q

1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, more...

integer, monotonic, +, A000142

a(n)=n!
n≥0
2 operations
Combinatoric
a(n)=n*a(n-1)
a(0)=1
n≥0
3 operations
Recursive
a(n)=∏[C(n, a(n-1))]
a(0)=1
C(n,k)=binomial coefficient
∏(a)=partial products of a
n≥0
4 operations
Combinatoric
a(n)=lcm(n!, a(n-1))
a(0)=1
lcm(a,b)=least common multiple
n≥0
4 operations
Combinatoric
a(n)=n*lcm(a(n-1), a(n-2))
a(0)=1
a(1)=1
lcm(a,b)=least common multiple
n≥0
5 operations
Recursive

Sequence btuzaf21som1g

1, 1, 5, 4, 2, 305, 1, 8, 2, 1, 4, 6, 14, 3, 1, 13, 5, 1, 7, 23, 1, 16, 4, 1, 1, 1, 1, 1, 2, 17, 1, 3, 1, 1, 1, 29, 1, 6, 1, 3, 1, 1, 1, 1, 3, 2, 5, 1, 63, 2, more...

integer, non-monotonic, +, A019712

a(n)=contfrac[Tribonacci]
Tribonacci=1.8392... (Tribonacci)
contfrac(a)=continued fraction of a
n≥0
2 operations
DecimalConstant

Sequence e0lrvyu1r0vmm

1, 1.543080634815244, 3.7621956910836314, 10.067661995777765, 27.308232836016487, 74.20994852478785, 201.7156361224559, 548.317035155212, 1490.479161252178, 4051.5420254925943, 11013.232920103324, 29937.070865949758, 81377.39571257407, 221206.6960055904, 601302.1420828041, 1634508.6862362083, 4443055.260253992, 12077476.37678767, 32829984.568665262, 89241150.48159364, 242582597.70489514, 659407867.2416073, 1792456423.065796, 4872401723.124452, 13244561064.921736, more...

decimal, strictly-monotonic, +

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

Sequence zmyrhgo0sugfg

1, 1.5574077246549023, 74.68593339876537, -0.8635188548774503, -1.1698563550584242, -2.35903773417943, 0.9943296190225849, 1.5381535569209899, 30.6237735079718, -1.013601814346662, -1.605012367826759, 29.214651770673843, 1.3701487455122843, 4.91679999052104, -4.823776826089959, 8.940480157748263, -0.5260857888567784, -0.5806710619667708, -0.656127983201063, -0.7699191877094069, -0.969511543661403, -1.4576737054682187, -8.8022251344211, 0.7177699669114329, 0.8731301134190125, more...

decimal, non-monotonic, +-

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

Sequence k0beacn12pjwc

1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 6, 2, 4, 4, 5, 2, 6, 2, 6, 4, 4, 2, 8, 3, 4, 4, 6, 2, 8, 2, 6, 4, 4, 4, 9, 2, 4, 4, 8, 2, 8, 2, 6, 6, 4, 2, 10, 3, 6, more...

integer, non-monotonic, +, A000005

a(n)=τ(n)
τ(n)=number of divisors of n
n≥1
2 operations
Prime
a(n)=Ω(floor(2^τ(n)))
τ(n)=number of divisors of n
Ω(n)=max distinct factors of n
n≥1
6 operations
Prime
a(n)=τ(n*p(n))/2
p(n)=nth prime
τ(n)=number of divisors of n
n≥1
7 operations
Prime

Sequence gekakw1rgdk0j

1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, 2, 17, 2, 19, 2, 3, 2, 23, 2, 5, 2, 3, 2, 29, 2, 31, 2, 3, 2, 5, 2, 37, 2, 3, 2, 41, 2, 43, 2, 3, 2, 47, 2, 7, 2, more...

integer, non-monotonic, +, A020639

a(n)=lpf(n)
lpf(n)=least prime factor of n
n≥1
2 operations
Prime
a(n)=gcd(n, lpf(n))
lpf(n)=least prime factor of n
gcd(a,b)=greatest common divisor
n≥1
4 operations
Prime
a(n)=gpf(lpf(n)²)
lpf(n)=least prime factor of n
gpf(n)=greatest prime factor of n
n≥1
4 operations
Prime
a(n)=exp(Λ(lpf(n)))
lpf(n)=least prime factor of n
Λ(n)=Von Mangoldt's function
n≥1
4 operations
Prime

Sequence qxbjop1xs1vff

1, 2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 3, 13, 7, 5, 2, 17, 3, 19, 5, 7, 11, 23, 3, 5, 13, 3, 7, 29, 5, 31, 2, 11, 17, 7, 3, 37, 19, 13, 5, 41, 7, 43, 11, 5, 23, 47, 3, 7, 5, more...

integer, non-monotonic, +, A006530

a(n)=gpf(n)
gpf(n)=greatest prime factor of n
n≥1
2 operations
Prime
a(n)=gcd(n, gpf(n))
gpf(n)=greatest prime factor of n
gcd(a,b)=greatest common divisor
n≥1
4 operations
Prime
a(n)=lpf(gpf(n)²)
gpf(n)=greatest prime factor of n
lpf(n)=least prime factor of n
n≥1
4 operations
Prime
a(n)=exp(Λ(gpf(n)))
gpf(n)=greatest prime factor of n
Λ(n)=Von Mangoldt's function
n≥1
4 operations
Prime
a(n)=floor(sqrt(floor(gpf(n)²)))
gpf(n)=greatest prime factor of n
n≥1
6 operations
Prime

Sequence r0cho0bzrtaxc

1, 2, 5, 5, 4, 1, 1, 18, 1, 1, 1, 1, 1, 2, 13, 3, 1, 2, 4, 16, 4, 3, 12, 1, 2, 2, 1, 1, 15, 1, 1, 1, 2, 2, 1, 4, 5, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, more...

integer, non-monotonic, +, A074269

a(n)=contfrac[Backhouse]
Backhouse=1.456... (Backhouse)
contfrac(a)=continued fraction of a
n≥0
2 operations
DecimalConstant

Sequence pqpjig3sq3dmp

1, 2, 8, 2, 4, 2, 7, 1, 2, 9, 1, 0, 0, 6, 2, 2, 6, 3, 6, 8, 7, 5, 3, 4, 2, 5, 6, 8, 8, 6, 9, 7, 9, 1, 7, 2, 7, 7, 6, 7, 6, 8, 8, 9, 2, 7, 3, 2, 5, 0, more...

integer, non-monotonic, +, A074962

a(n)=de[GlaisherKinkelin]
GlaisherKinkelin=1.2824... (Glaisher-Kinkelin)
de(a)=decimal expansion of a
n≥0
2 operations
DecimalConstant

Sequence e2us3gqeu1boh

1, 2.718281828459045, 7.38905609893065, 20.085536923187668, 54.598150033144236, 148.4131591025766, 403.4287934927351, 1096.6331584284585, 2980.9579870417283, 8103.083927575384, 22026.465794806718, 59874.14171519782, 162754.79141900392, 442413.3920089205, 1202604.2841647768, 3269017.3724721107, 8886110.520507872, 24154952.7535753, 65659969.13733051, 178482300.96318725, 485165195.4097903, 1318815734.4832146, 3584912846.131592, 9744803446.248903, 26489122129.84347, more...

decimal, strictly-monotonic, +

a(n)=exp(n)
n≥0
2 operations
Power

Sequence 5jttb1vusgdqd

1, 3, 1, 1, 5, 1, 1, 1, 3, 12, 4, 1, 271, 1, 1, 2, 7, 1, 35, 6, 1, 9, 4, 2, 1, 1, 2, 1, 1, 2, 15, 3, 1, 24, 2, 39, 1, 3, 1, 2, 2, 5, 1, 2, 2, 1, 3, 3, 1, 3, more...

integer, non-monotonic, +, A087501

a(n)=contfrac[GlaisherKinkelin]
GlaisherKinkelin=1.2824... (Glaisher-Kinkelin)
contfrac(a)=continued fraction of a
n≥0
2 operations
DecimalConstant

Sequence n55c2fon5zb

1, 3, 3, 2, 5, 8, 2, 2, 7, 5, 7, 3, 3, 2, 2, 0, 8, 8, 1, 7, 6, 5, 8, 2, 8, 7, 7, 6, 0, 7, 1, 0, 2, 7, 7, 4, 8, 8, 3, 8, 4, 5, 9, 4, 8, 9, 0, 4, 2, 4, more...

integer, non-monotonic, +, A083343

a(n)=de[B3]
B3=1.3325... (Mertens B3)
de(a)=decimal expansion of a
n≥0
2 operations
DecimalConstant

Sequence sbudzke0snrw

1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 14, 24, 24, 31, 18, 39, 20, 42, 32, 36, 24, 60, 31, 42, 40, 56, 30, 72, 32, 63, 48, 54, 48, 91, 38, 60, 56, 90, 42, 96, 44, 84, 78, 72, 48, 124, 57, 93, more...

integer, non-monotonic, +, A000203

a(n)=σ(n)
σ(n)=divisor sum of n
n≥1
2 operations
Prime

Sequence tj23qg0wt21zd

1, 3, 147, 1, 1, 1, 1, 5, 1, 5, 1, 2, 1, 1, 1, 1, 1, 3, 45, 1, 1, 2, 4, 8, 3, 2, 1, 1, 1, 4, 1, 6, 1, 4, 1, 64, 1, 1, 16, 4, 1, 1, 1, 1, 10, 5, 1, 1, 7, 4, more...

integer, non-monotonic, +

a(n)=contfrac[B3]
B3=1.3325... (Mertens B3)
contfrac(a)=continued fraction of a
n≥0
2 operations
DecimalConstant

Sequence ax4hv2yzrhzsf

1, 4, 5, 6, 0, 7, 4, 9, 4, 8, 5, 8, 2, 6, 8, 9, 6, 7, 1, 3, 9, 9, 5, 9, 5, 3, 5, 1, 1, 1, 6, 5, 4, 3, 5, 5, 7, 6, 5, 3, 1, 7, 8, 3, 7, 4, 8, 4, 7, 1, more...

integer, non-monotonic, +, A072508

a(n)=de[Backhouse]
Backhouse=1.456... (Backhouse)
de(a)=decimal expansion of a
n≥0
2 operations
DecimalConstant

Sequence kbpwb2bxbeqcf

1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, more...

integer, strictly-monotonic, +, A018252

a(n)=composite(n)
composite(n)=nth composite number
n≥1
2 operations
Prime

Sequence wqwhagpwcscgc

1, 6, 1, 8, 0, 3, 3, 9, 8, 8, 7, 4, 9, 8, 9, 4, 8, 4, 8, 2, 0, 4, 5, 8, 6, 8, 3, 4, 3, 6, 5, 6, 3, 8, 1, 1, 7, 7, 2, 0, 3, 0, 9, 1, 7, 9, 8, 0, 5, 7, more...

integer, non-monotonic, +, A001622

a(n)=de[ϕ]
ϕ=1.618... (Golden Ratio)
de(a)=decimal expansion of a
n≥0
2 operations
DecimalConstant
a(n)=de[sqrt(1+ϕ)]
ϕ=1.618... (Golden Ratio)
de(a)=decimal expansion of a
n≥0
5 operations
Power
a(n)=de[2*5*ϕ]
ϕ=1.618... (Golden Ratio)
de(a)=decimal expansion of a
n≥0
6 operations
Arithmetic

Sequence e2tkwlio5ubrf

1, 6, 6, 1, 6, 8, 7, 9, 4, 9, 6, 3, 3, 5, 9, 4, 1, 2, 1, 2, 9, 5, 8, 1, 8, 9, 2, 2, 7, 4, 9, 9, 5, 0, 7, 4, 9, 9, 6, 4, 4, 1, 8, 6, 3, 5, 0, 2, 5, 0, more...

integer, non-monotonic, +, A112302

a(n)=de[QR]
QR=1.6616... (Quadratic Recurrence)
de(a)=decimal expansion of a
n≥0
2 operations
DecimalConstant

Sequence 5ikbvw505eq1k

1, 8, 3, 9, 2, 8, 6, 7, 5, 5, 2, 1, 4, 1, 6, 1, 1, 3, 2, 5, 5, 1, 8, 5, 2, 5, 6, 4, 6, 5, 3, 2, 8, 6, 6, 0, 0, 4, 2, 4, 1, 7, 8, 7, 4, 6, 0, 9, 7, 5, more...

integer, non-monotonic, +, A058265

a(n)=de[Tribonacci]
Tribonacci=1.8392... (Tribonacci)
de(a)=decimal expansion of a
n≥0
2 operations
DecimalConstant

Sequence daje0xynhaqee

1.5707963267948966, 0.7853981633974483, 0.46364760900080615, 0.32175055439664213, 0.244978663126864, 0.19739555984988066, 0.1651486774146267, 0.1418970546041638, 0.12435499454676147, 0.11065722117389565, 0.09966865249116186, 0.09065988720074514, 0.08314123188844125, 0.0767718912697779, 0.07130746478529026, 0.06656816377582375, 0.06241880999595728, 0.05875582271572255, 0.05549850524571687, 0.05258306161094173, 0.04995839572194272, 0.04758310327698334, 0.04542327942157698, 0.043450895391530686, 0.04164257909858837, more...

decimal, strictly-monotonic, convergent, +

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

Sequence 1pozvmadxjihf

1.6449340668482264, 1.2020569031595942, 1.0823232337111381, 1.03692775514337, 1.0173430619844492, 1.008349277381923, 1.0040773561979444, 1.0020083928260821, 1.000994575127818, 1.0004941886041194, 1.000246086553308, 1.0001227133475785, 1.0000612481350588, 1.000030588236307, 1.0000152822594086, 1.0000076371976379, 1.000003817293265, 1.0000019082127165, more...

decimal, strictly-monotonic, +

a(n)=ζ(n)
ζ(n)=Riemann zeta
n≥2
2 operations
Prime

Sequence xr3nzyt1pcwvm

2, -2.185039863261519, 1.4179285755053868, 6.490566602728474, 0.21040629391697788, 0.21356723292044746, 0.2168745891178323, 0.22034000376284393, 0.22397645454871787, 0.22779845932374504, 0.23182231905201484, 0.23606640927074993, 0.24055153190462047, 0.2453013427722584, 0.250342874794811, 0.25570718327303055, 0.2614301483439144, 0.26755348190833933, 0.2741260035181865, 0.28120527434983683, 0.2888597142589457, 0.29717138004773413, 0.30623966332012453, 0.3161862900768629, 0.3271621996737142, more...

decimal, non-monotonic, +-

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

Sequence nidxhjsebrrlb

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

Sequence d3iagnfw0qw5

2, -0.45765755436028577, -2.0303137983814556, 0.49484793829887097, 1.8531163265557713, -0.2900678418018812, -3.350233348793712, -4.723179246621436, 0.01079068502592696, 92.66892549777648, 0.008057957518507039, 124.09824127886377, -0.005331512582201638, -187.56225546790253, 0.7406536784433513, 1.0937461641873407, 0.5168672339692599, 1.7592950361976771, -0.1907634670415232, -5.178351237736626, 0.5028966679958746, 1.8179516659029487, -0.25231398108125785, -3.878852056639137, -1.1012287532956417, more...

decimal, non-monotonic, +-

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

Sequence wma1ci0fdudz

2, -0.4161468365471424, 0.9146533258523714, 0.6100652997429745, 0.8196106080000903, 0.6825058578960018, 0.7759946131215992, 0.7137247340083882, 0.7559287135747029, 0.7276347923146813, 0.7467496017309728, 0.7339005972426009, 0.7425675503014617, 0.7367348583938166, 0.740666263873949, 0.7380191411807893, 0.7398027782109352, 0.7386015286351051, 0.7394108086387853, 0.7388657151407354, 0.7392329180769628, 0.7389855754839373, 0.7391521928375896, 0.7390399593850235, 0.7391155620964187, more...

decimal, non-monotonic, +-

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

Sequence wqaew4bmkyozo

2, 0.46364760900080615, 1.1366511866264786, 0.7215293734239171, 0.9457667771079381, 0.8132633659430815, 0.8880201279546327, 0.844639503352005, 0.8694225508555931, 0.8551339813983643, 0.8633292625846987, 0.8586146570923905, 0.8613222220676018, 0.8597657434911755, 0.8606599960381842, 0.8601460477898633, 0.8604413705582306, 0.8602716550961863, 0.8603691807612092, 0.860313136399174, 0.860345342343114, 0.8603268349498331, 0.8603374702936364, 0.860331358629162, 0.8603348707261661, more...

decimal, non-monotonic, +

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

Sequence xtxnqttmlzdtb

2, 0.9092974268256817, 0.7890723435728884, 0.7097000402345258, 0.6516062636498291, 0.606464344938615, 0.5699658928122394, 0.5396033335454621, 0.513795726952195, 0.49148642206518095, 0.4719368868058549, 0.4546123016451699, 0.43911402646395187, 0.4251377119701682, 0.41244623877209624, 0.40085162960706694, 0.3902026038089464, 0.3803757974172909, 0.3712694329849674, 0.3627986673680121, 0.35489211415615574, 0.34748920443044273, 0.3405381562584766, 0.3339943931488303, 0.3278192983231869, more...

decimal, strictly-monotonic, convergent, +

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

Sequence zilqtufnzufld

2, 0.9640275800758169, 0.7460679984455996, 0.6327973151866226, 0.5599753773221933, 0.5079591636537706, 0.4683535539050593, 0.43686805781587285, 0.41104502163463524, 0.3893596361728678, 0.37080804437538006, 0.3546982984383307, 0.34053563213946997, 0.3279555010749178, 0.31668250906136897, 0.3065041555904077, 0.29725346547700154, 0.28879715089658653, 0.28102733511234973, 0.27385563581351396, 0.2672088513983159, 0.2610257605746587, 0.2552547106097325, 0.2498517741988791, 0.24477932289222054, more...

decimal, strictly-monotonic, convergent, +

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

Sequence dodcahtwj3i1g

2, 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, 1, 10, 1, 1, 12, 1, 1, 14, 1, 1, 16, 1, 1, 18, 1, 1, 20, 1, 1, 22, 1, 1, 24, 1, 1, 26, 1, 1, 28, 1, 1, 30, 1, 1, 32, 1, 1, more...

integer, non-monotonic, +, A003417

a(n)=contfrac[e]
e=2.7182... (Euler e)
contfrac(a)=continued fraction of a
n≥0
2 operations
DecimalConstant
a(n)=contfrac[root(log(2), 2)]
root(n,a)=the n-th root of a
contfrac(a)=continued fraction of a
n≥0
5 operations
Power

Sequence wt1tbgmgmbojn

2, 1, 2, 5, 1, 1, 2, 1, 1, 3, 10, 2, 1, 3, 2, 24, 1, 3, 2, 3, 1, 1, 1, 90, 2, 1, 12, 1, 1, 1, 1, 5, 2, 6, 1, 6, 3, 1, 1, 2, 5, 2, 1, 2, 1, 1, 4, 1, 2, 2, more...

integer, non-monotonic, +, A002211

a(n)=contfrac[Khintchine]
Khintchine=2.6854... (Khintchine)
contfrac(a)=continued fraction of a
n≥0
2 operations
DecimalConstant

Sequence az24rzxjrh0gm

2, 1.1071487177940904, 0.8362045005428747, 0.6964303446320494, 0.60832620268374, 0.5465192259241443, 0.500166904320852, 0.4637811235430327, 0.4342550258756114, 0.4096835485780686, 0.3888262897253467, 0.3708369119819261, 0.3551158536324048, 0.3412250829553423, 0.3288362346656749, 0.3176977199569499, 0.30761312567191645, 0.29842659613071176, 0.2900126803237685, 0.2822691185784435, 0.2751116140125213, 0.26846997460349015, 0.2622852208893549, 0.256507386302984, 0.25109382243214373, more...

decimal, strictly-monotonic, convergent, +

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

Sequence l2ff0du3kwl3n

2, 1.4142135623730951, 1.189207115002721, 1.0905077326652577, 1.0442737824274138, 1.0218971486541166, 1.0108892860517005, 1.0054299011128027, 1.0027112750502025, 1.0013547198921082, 1.0006771306930664, 1.0003385080526823, 1.0001692397053021, 1.0000846162726942, 1.0000423072413958, 1.0000211533969647, 1.0000105766425498, 1.0000052883072919, 1.0000026441501502, 1.0000013220742012, 1.0000006610368821, 1.0000003305183864, 1.0000001652591797, 1.0000000826295865, 1.0000000413147925, more...

decimal, strictly-monotonic, convergent, +

a(n)=sqrt(a(n-1))
a(0)=2
n≥0
2 operations
Recursive
a(n)=root(4, a(n-1)²)
a(0)=2
root(n,a)=the n-th root of a
n≥0
4 operations
Recursive
a(n)=a(n-1)^(1/2)
a(0)=2
n≥0
5 operations
Recursive

Sequence ke34fnlkrp1fn

2, 3, 4, 7, 8, 15, 24, 60, 168, 480, 1512, 4800, 15748, 28672, 65528, more...

integer, strictly-monotonic, +, A007497

a(n)=σ(a(n-1))
a(0)=2
σ(n)=divisor sum of n
n≥0
2 operations
Prime

Sequence 3adjjx2yzeaxh

2, 3, 5, 7, 1, 1, 1, 3, 1, 7, 1, 9, 2, 3, 2, 9, 3, 1, 3, 7, 4, 1, 4, 3, 4, 7, 5, 3, 5, 9, 6, 1, 6, 7, 7, 1, 7, 3, 7, 9, 8, 3, 8, 9, 9, 7, 1, 0, 1, 1, more...

integer, non-monotonic, +, A033308

a(n)=de[CopelandErdős]
CopelandErdős=0.2357... (Copeland-Erdős)
de(a)=decimal expansion of a
n≥0
2 operations
DecimalConstant

Sequence 3obzf0s451s5l

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, more...

integer, strictly-monotonic, +, A000040

a(n)=p(n)
p(n)=nth prime
n≥1
2 operations
Prime
a(n)=gpf(floor(2*p(n)))
p(n)=nth prime
gpf(n)=greatest prime factor of n
n≥1
6 operations
Prime

Sequence vwnaql1adya0i

2, 4, 8, 14, 22, 33, 48, 66, 90, 120, 156, 202, 256, 322, 400, 494, 604, 734, 888, 1067, 1272, 1512, 1790, 2107, 2472, 2890, 3364, 3903, 4515, 5207, 5990, 6875, 7868, 8984, 10238, 11637, 13207, 14959, 16909, 19075, 21483, 24173, 27149, 30436, 34080, 38103, 42552, 47444, 52835, more...

integer, strictly-monotonic, +, A025003

a(n)=composite(a(n-1))
a(0)=2
composite(n)=nth composite number
n≥0
2 operations
Prime

Sequence n11quy32pwigm

2, 6, 1, 4, 9, 7, 2, 1, 2, 8, 4, 7, 6, 4, 2, 7, 8, 3, 7, 5, 5, 4, 2, 6, 8, 3, 8, 6, 0, 8, 6, 9, 5, 8, 5, 9, 0, 5, 1, 5, 6, 6, 6, 4, 8, 2, 6, 1, 1, 9, more...

integer, non-monotonic, +, A077761

a(n)=de[Mertens]
Mertens=0.2614... (Mertens)
de(a)=decimal expansion of a
n≥0
2 operations
DecimalConstant

Sequence 1w02asgugejep

2, 6, 8, 5, 4, 5, 2, 0, 0, 1, 0, 6, 5, 3, 0, 6, 4, 4, 5, 3, 0, 9, 7, 1, 4, 8, 3, 5, 4, 8, 1, 7, 9, 5, 6, 9, 3, 8, 2, 0, 3, 8, 2, 2, 9, 3, 9, 9, 4, 4, more...

integer, non-monotonic, +, A002210

a(n)=de[Khintchine]
Khintchine=2.6854... (Khintchine)
de(a)=decimal expansion of a
n≥0
2 operations
DecimalConstant

Sequence idcen5jpa2zpc

2, 7, 1, 8, 2, 8, 1, 8, 2, 8, 4, 5, 9, 0, 4, 5, 2, 3, 5, 3, 6, 0, 2, 8, 7, 4, 7, 1, 3, 5, 2, 6, 6, 2, 4, 9, 7, 7, 5, 7, 2, 4, 7, 0, 9, 3, 6, 9, 9, 9, more...

integer, non-monotonic, +, A001113

a(n)=de[e]
e=2.7182... (Euler e)
de(a)=decimal expansion of a
n≥0
2 operations
DecimalConstant
a(n)=de[root(log(2), 2)]
root(n,a)=the n-th root of a
de(a)=decimal expansion of a
n≥0
5 operations
Power
a(n)=de[2*5*e]
e=2.7182... (Euler e)
de(a)=decimal expansion of a
n≥0
6 operations
Arithmetic

Sequence sb0gkrb34xxsi

3, -7.015252551434534, -1.1127836396499338, -0.4929760630059242, -1.861445197641989, 0.2991195764453913, 3.242838238854065, 9.84320225497418, 2.2487882596280446, -0.8053455460881099, -0.9608803799719335, -0.698793757516798, -1.190152495237775, -0.40015945592409213, -2.364171319903177, 1.0160822861856584, 0.6196101009757935, 1.4018942755188502, 0.17052673375226393, 5.807230411232213, -1.9399389108821214, 0.3868770856397324, 2.4545358453016966, -1.218917531063782, -0.3671590959085158, more...

decimal, non-monotonic, +-

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

Sequence lbpnhcgrw2aym

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

Sequence vvfdypotcl5rp

3, -0.9899924966004454, 0.5486961336030971, 0.8532053115057471, 0.6575716719440715, 0.7914787496844161, 0.7027941118082985, 0.7630391877968155, 0.7227389047849776, 0.7499969196947133, 0.7316909685258258, 0.7440456819525395, 0.7357345682868414, 0.7413379612461033, 0.7375657269232188, 0.7401077700526904, 0.7383958863975352, 0.7395492425705096, 0.7387724239832232, 0.739295741775515, 0.7389432483650884, 0.7391807011172313, 0.739020754151705, 0.7391284981950723, 0.7390559213481233, more...

decimal, non-monotonic, convergent, +-

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

Sequence zwzup542ixjhh

3, -0.1425465430742778, -0.14351994778492885, -0.14451354178374737, -0.14552803216462146, -0.14656416116305784, -0.14762270843290942, -0.14870449350594378, -0.14981037845185682, -0.15094127075832087, -0.15209812645289802, -0.15328195349118695, -0.15449381543844776, -0.15573483547521702, -0.15700620076114324, -0.15830916719551408, -0.15964506461779163, -0.16101530249702162, -0.16242137616535007, -0.16386487365820682, -0.16534748323216025, -0.16687100164120944, -0.16843734326358908, -0.17004855018430143, -0.17170680335389196, more...

decimal, strictly-monotonic, +-

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

Sequence rk0tbhobmwhti

3, 0.1411200080598672, 0.14065207678644337, 0.14018878179601915, 0.13973004691077978, 0.1392757976957311, 0.13882596140772388, 0.1383804669462898, 0.1379392448062136, 0.13750222703176954, 0.13706934717255298, 0.13664054024084255, 0.1362157426704298, 0.1357948922768576, 0.13537792821901018, 0.1349647909620012, 0.13455542224130787, 0.13414976502810239, 0.13374776349573347, 0.1333493629873131, 0.13295450998436578, 0.13256315207649932, 0.132175237932058, 0.1317907172697207, 0.1314095408310083, more...

decimal, strictly-monotonic, convergent, +

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

Sequence 42zyqj1ugnlfo

3, 0.32175055439664213, 1.25950624160801, 0.671048329612308, 0.9797663957344107, 0.7956180054304229, 0.8987330497592796, 0.8386816386458731, 0.8729099645744918, 0.8531512908469421, 0.8644756184318187, 0.8579582189693987, 0.8617002118824961, 0.8595487824794827, 0.8607847572160703, 0.8600743806853275, 0.8604825635308438, 0.8602479863443071, 0.8603827831250737, 0.860305320057476, 0.8603498341528393, 0.8603242537436738, 0.8603389536090192, 0.8603305062381361, 0.8603353605584022, more...

decimal, non-monotonic, +

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

Sequence p0ckdpwq0kxt

3, 0.9950547536867305, 0.7595094447988621, 0.640787923324476, 0.5654358019788175, 0.511999429294464, 0.4715015927907331, 0.4394117751122899, 0.4131567449838749, 0.39114974578176415, 0.3723509905730575, 0.35604638636071295, 0.3417268421246582, 0.32901817504470154, 0.31763828777609904, 0.30736988998678955, 0.29804250065927596, 0.2895202126358343, 0.28169315665410155, 0.27447141042680046, 0.26778056521076327, 0.2615584414311782, 0.255752616915406, 0.2503185401452386, 0.24521807150121974, more...

decimal, strictly-monotonic, convergent, +

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

Sequence xecz0440luoph

3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8, 4, 6, 2, 6, 4, 3, 3, 8, 3, 2, 7, 9, 5, 0, 2, 8, 8, 4, 1, 9, 7, 1, 6, 9, 3, 9, 9, 3, 7, 5, 1, more...

integer, non-monotonic, +, A000796

a(n)=de[π]
π=3.1415... (Pi)
de(a)=decimal expansion of a
n≥0
2 operations
DecimalConstant
a(n)=de[acos(-1)]
de(a)=decimal expansion of a
n≥0
4 operations
Trigonometric
a(n)=de[exp(abs(log(π)))]
π=3.1415... (Pi)
de(a)=decimal expansion of a
n≥0
5 operations
Power
a(n)=de[2*5*π]
π=3.1415... (Pi)
de(a)=decimal expansion of a
n≥0
6 operations
Arithmetic

Sequence wzn1rwctom2lc

3, 1.2490457723982544, 0.8956828296697594, 0.7304247981836736, 0.6308548217686205, 0.562798449988655, 0.5126161471164168, 0.47368951138857185, 0.4423785524051386, 0.41649788124377884, 0.39464729391709885, 0.3758834754182548, 0.3595449989973961, 0.3451527238482953, 0.3323500237088844, 0.32086531482643227, 0.310487684522248, 0.301050535688147, 0.29242030979978, 0.284488525933727, 0.2771660428335162, 0.27037884640508975, 0.2640649058334994, 0.2581717923076575, 0.2526548511259183, more...

decimal, strictly-monotonic, convergent, +

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

Sequence 45e5bvr3z2z3c

3, 1.7320508075688772, 1.3160740129524924, 1.147202690439877, 1.0710754830729146, 1.0349277670798647, 1.0173139963058921, 1.0086198472694716, 1.0043006757288733, 1.0021480308461785, 1.0010734392871377, 1.000536575686835, 1.0002682518638863, 1.0001341169382667, 1.000067056220865, 1.0000335275483843, 1.0000167636336825, 1.000008381781714, 1.0000041908820754, 1.0000020954388422, 1.0000010477188723, 1.000000523859299, 1.0000002619296153, 1.000000130964799, 1.0000000654823973, more...

decimal, strictly-monotonic, convergent, +

a(n)=sqrt(a(n-1))
a(0)=3
n≥0
2 operations
Recursive
a(n)=root(4, a(n-1)²)
a(0)=3
root(n,a)=the n-th root of a
n≥0
4 operations
Recursive
a(n)=a(n-1)^(1/2)
a(0)=3
n≥0
5 operations
Recursive

Sequence nh2klcrdlym2h

3, 4, 0, 5, 3, 7, 3, 2, 9, 5, 5, 0, 9, 9, 9, 1, 4, 2, 8, 2, 6, 2, 7, 3, 1, 8, 4, 4, 3, 2, 9, 0, 2, 8, 9, 6, 7, 1, 0, 6, 0, 8, 2, 1, 7, 1, 2, 4, 3, 0, more...

integer, non-monotonic, +, A086230

a(n)=de[Pólya_D3]
Pólya_D3=0.3405... (Pólya random walk 3D)
de(a)=decimal expansion of a
n≥0
2 operations
DecimalConstant

Sequence gom1wdmvwqgjj

3, 4, 7, 8, 15, 24, 60, 168, 480, 1512, 4800, 15748, 28672, 65528, more...

integer, strictly-monotonic, +

a(n)=σ(a(n-1))
a(0)=3
σ(n)=divisor sum of n
n≥0
2 operations
Prime

Sequence gw2idni12ytnj

3, 5, 11, 31, 127, 709, 5381, 52711, 648391, more...

integer, strictly-monotonic, +

a(n)=p(a(n-1))
a(0)=3
p(n)=nth prime
n≥0
2 operations
Prime
a(n)=or(1, p(a(n-1)))
a(0)=3
p(n)=nth prime
or(a,b)=bitwise or
n≥0
4 operations
Prime

Sequence tlhn5ayr44tyj

3, 6, 10, 16, 25, 36, 51, 70, 94, 124, 161, 207, 262, 328, 407, 502, 614, 746, 900, 1080, 1288, 1529, 1808, 2127, 2494, 2915, 3393, 3939, 4556, 5253, 6040, 6930, 7931, 9056, 10322, 11729, 13308, 15067, 17031, 19208, 21637, 24340, 27330, 30633, 34296, 38344, 42820, 47742, 53166, more...

integer, strictly-monotonic, +, A025004

a(n)=composite(a(n-1))
a(0)=3
composite(n)=nth composite number
n≥0
2 operations
Prime

Sequence evxmhr5g4b0go

3, 7, 3, 9, 5, 5, 8, 1, 3, 6, 1, 9, 2, 0, 2, 2, 8, 8, 0, 5, 4, 7, 2, 8, 0, 5, 4, 3, 4, 6, 4, 1, 6, 4, 1, 5, 1, 1, 1, 6, 2, 9, 2, 4, 8, 6, 0, 6, 1, 5, more...

integer, non-monotonic, +, A005596

a(n)=de[Artins]
Artins=0.3739... (Artins)
de(a)=decimal expansion of a
n≥0
2 operations
DecimalConstant

Sequence dc212nwugb3uj

3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1, 1, 15, 3, 13, 1, 4, 2, 6, 6, 99, 1, 2, 2, 6, 3, 5, 1, 1, 6, 8, 1, 7, 1, 2, 3, 7, more...

integer, non-monotonic, +, A001203

a(n)=contfrac[π]
π=3.1415... (Pi)
contfrac(a)=continued fraction of a
n≥0
2 operations
DecimalConstant
a(n)=contfrac[acos(-1)]
contfrac(a)=continued fraction of a
n≥0
4 operations
Trigonometric
a(n)=contfrac[exp(abs(log(π)))]
π=3.1415... (Pi)
contfrac(a)=continued fraction of a
n≥0
5 operations
Power

Sequence u5xe2d4xly4jg

3, 9, 81, 6561, 43046721, 1853020188851841, more...

integer, strictly-monotonic, +, A011764

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

Sequence g5rnsvn0x45rg

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

Sequence b4ytrhgeb1rvm

4, -0.7568024953079282, -0.6866002607386249, -0.6339114732985194, -0.5923008210655263, -0.5582713944195423, -0.529720835124789, -0.5052924560809323, -0.4840633697270739, -0.4653795417340422, -0.4487620117263402, -0.4338504581249109, -0.4203676380717351, -0.40809611175335475, -0.3968625110465547, -0.3865266116719075, -0.37697355987444925, -0.36810822709513386, -0.3598510343307839, -0.3521348128703309, -0.3449024095242504, -0.3381048356363251, -0.3316998192805959, -0.32565066049373903, -0.3199253171119008, more...

decimal, non-monotonic, convergent, +-

a(n)=sin(a(n-1))
a(0)=4
n≥0
2 operations
Trigonometric

Sequence 5ygvhkm41iqgo

4, -0.6536436208636119, 0.7938734492261525, 0.7010885250960164, 0.7641404871774221, 0.7219773353286648, 0.7505004356582367, 0.7313476609259477, 0.7442750117780783, 0.7355792307316547, 0.7414422042900879, 0.7374953301579025, 0.7401551092185018, 0.73836396157563, 0.739570730869702, 0.7387579416665603, 0.7393054938130885, 0.7389366777222988, 0.7391851264762225, 0.7390177728568568, 0.7391305062860009, 0.7390545686080692, 0.7391057215569367, 0.7390712645038388, 0.7390944752748578, more...

decimal, non-monotonic, +-

a(n)=cos(a(n-1))
a(0)=4
n≥0
2 operations
Trigonometric

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