Sequence Database

A database with 899757 machine generated integer and decimal sequences.

Displaying result 0-99 of total 75555. [0] [1] [2] [3] [4] ... [755]

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)=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)=∑(gcd(n, n²))
gcd(a,b)=greatest common divisor
∑(a)=partial sums of a
n≥0
5 operations
Divisibility
a(n)=∑(sqrt(n*n))
∑(a)=partial sums of a
n≥0
5 operations
Power
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)=n%p(p(n))+a(n-1)
a(0)=0
p(n)=nth prime
n≥0
7 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)=∑(-n)
∑(a)=partial sums of a
n≥0
3 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)=-∑(C(n, a(n-1)))
a(0)=0
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=a(n-1)-n%p(p(n))
a(0)=0
p(n)=nth prime
n≥0
7 operations
Prime

Sequence h3vrmorpscwhg

0, 1, 5, 14, 30, 55, 91, 140, 204, 285, 385, 506, 650, 819, 1015, 1240, 1496, 1785, 2109, 2470, 2870, 3311, 3795, 4324, 4900, 5525, 6201, 6930, 7714, 8555, 9455, 10416, 11440, 12529, 13685, 14910, 16206, 17575, 19019, 20540, 22140, 23821, 25585, 27434, 29370, 31395, 33511, 35720, 38024, 40425, more...

integer, strictly-monotonic, +, A000330

a(n)=∑(n²)
∑(a)=partial sums of a
n≥0
3 operations
Arithmetic
a(n)=n²+a(n-1)
a(0)=0
n≥0
4 operations
Recursive
a(n)=∑(lcm(n, n²))
lcm(a,b)=least common multiple
∑(a)=partial sums of a
n≥0
5 operations
Divisibility
a(n)=n^(1+1)+a(n-1)
a(0)=0
n≥0
7 operations
Power

Sequence rh2c2v1qn0g5g

0, 1, 9, 36, 100, 225, 441, 784, 1296, 2025, 3025, 4356, 6084, 8281, 11025, 14400, 18496, 23409, 29241, 36100, 44100, 53361, 64009, 76176, 90000, 105625, 123201, 142884, 164836, 189225, 216225, 246016, 278784, 314721, 354025, 396900, 443556, 494209, 549081, 608400, 672400, 741321, 815409, 894916, 980100, 1071225, 1168561, 1272384, 1382976, 1500625, more...

integer, strictly-monotonic, +, A000537

a(n)=∑(n)²
∑(a)=partial sums of a
n≥0
3 operations
Arithmetic
a(n)=∑(n^3)
∑(a)=partial sums of a
n≥0
4 operations
Power
a(n)=∑(1+a(n-1))²
a(0)=0
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑(C(n, a(n-1)))²
a(0)=0
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric

Sequence avvwp50xazwz

0, 1, 2, 2, 3, 4, 8, 3, 4, 12, 11, 6, 10, 19, 18, 4, 5, 24, 34, 11, 18, 24, 13, 14, 18, 39, 28, 20, 31, 46, 32, 5, 6, 40, 69, 36, 46, 33, 62, 20, 29, 66, 42, 37, 24, 38, 53, 22, 26, 89, more...

integer, non-monotonic, +

a(n)=stern(∑(n))
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
n≥0
3 operations
Recursive
a(n)=stern(lcm(∑(n), 2))
∑(a)=partial sums of a
lcm(a,b)=least common multiple
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Divisibility
a(n)=stern(∑(C(n, a(n-1))))
a(0)=0
C(n,k)=binomial coefficient
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Combinatoric

Sequence mrr5xzcftqxsg

0, 1, 2, 4, 5, 8, 10, 13, 14, 18, 21, 26, 28, 33, 36, 40, 41, 46, 50, 57, 60, 68, 73, 80, 82, 89, 94, 102, 105, 112, 116, 121, 122, 128, 133, 142, 146, 157, 164, 174, 177, 188, 196, 209, 214, 226, 233, 242, 244, 253, more...

integer, strictly-monotonic, +, A174868

a(n)=∑(stern(n))
stern(n)=Stern-Brocot sequence
∑(a)=partial sums of a
n≥0
3 operations
Recursive
a(n)=∑(stern(lcm(n, 2)))
lcm(a,b)=least common multiple
stern(n)=Stern-Brocot sequence
∑(a)=partial sums of a
n≥0
5 operations
Divisibility

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)=1-∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=a(n-1)^(2-1)-n
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 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)=1+∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=∑(C(n, a(n-1)))
a(0)=1
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
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+a(n-1)%p(a(n-1))
a(0)=1
p(n)=nth prime
n≥0
6 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)=2-∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=a(n-1)%(2*a(n-1))-n
a(0)=2
n≥0
7 operations
Divisibility

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)=2+∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=n%a(n-1)+a(n-1)
a(0)=2
n≥0
5 operations
Divisibility
a(n)=∑(C(n, a(n-1)))
a(0)=2
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=∑(∑(μ(abs(a(n-1)))))
a(0)=2
μ(n)=Möbius function
∑(a)=partial sums of a
n≥0
5 operations
Prime

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
a(n)=3-∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

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)=3+∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=n%a(n-1)+a(n-1)
a(0)=3
n≥0
5 operations
Divisibility
a(n)=∑(C(n, a(n-1)))
a(0)=3
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=(n+a(n-1))%p(a(n-1))
a(0)=3
p(n)=nth prime
n≥0
6 operations
Prime

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
a(n)=4-∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=(a(n-1)-n)%(n*a(n-1))
a(0)=4
n≥0
7 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)=4+∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=n%a(n-1)+a(n-1)
a(0)=4
n≥0
5 operations
Divisibility
a(n)=∑(C(n, a(n-1)))
a(0)=4
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=(n+a(n-1))%p(a(n-1))
a(0)=4
p(n)=nth prime
n≥0
6 operations
Prime

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
a(n)=5-∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

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)=5+∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=n%a(n-1)+a(n-1)
a(0)=5
n≥0
5 operations
Divisibility
a(n)=∑(C(n, a(n-1)))
a(0)=5
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=(n+a(n-1))%p(a(n-1))
a(0)=5
p(n)=nth prime
n≥0
6 operations
Prime

Sequence asegayfwttyyd

-10, -19, -27, -34, -40, -45, -49, -52, -54, -55, -55, -54, -52, -49, -45, -40, -34, -27, -19, -10, 0, 11, 23, 36, 50, 65, 81, 98, 116, 135, 155, 176, 198, 221, 245, 270, 296, 323, 351, 380, 410, 441, 473, 506, 540, 575, 611, 648, 686, 725, more...

integer, non-monotonic, +-

a(n)=∑(n-10)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence g3oeqze35sqgm

-10, -9, -7, -4, 0, 5, 11, 18, 26, 35, 45, 56, 68, 81, 95, 110, 126, 143, 161, 180, 200, 221, 243, 266, 290, 315, 341, 368, 396, 425, 455, 486, 518, 551, 585, 620, 656, 693, 731, 770, 810, 851, 893, 936, 980, 1025, 1071, 1118, 1166, 1215, more...

integer, strictly-monotonic, +-

a(n)=∑(n)-10
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence to010whxa40ak

-9, -17, -24, -30, -35, -39, -42, -44, -45, -45, -44, -42, -39, -35, -30, -24, -17, -9, 0, 10, 21, 33, 46, 60, 75, 91, 108, 126, 145, 165, 186, 208, 231, 255, 280, 306, 333, 361, 390, 420, 451, 483, 516, 550, 585, 621, 658, 696, 735, 775, more...

integer, non-monotonic, +-

a(n)=∑(n-9)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence oj0ltlnkd0c2j

-9, -8, -6, -3, 1, 6, 12, 19, 27, 36, 46, 57, 69, 82, 96, 111, 127, 144, 162, 181, 201, 222, 244, 267, 291, 316, 342, 369, 397, 426, 456, 487, 519, 552, 586, 621, 657, 694, 732, 771, 811, 852, 894, 937, 981, 1026, 1072, 1119, 1167, 1216, more...

integer, strictly-monotonic, +-

a(n)=∑(n)-9
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence t5z1cpf1nvbqi

-8, -15, -21, -26, -30, -33, -35, -36, -36, -35, -33, -30, -26, -21, -15, -8, 0, 9, 19, 30, 42, 55, 69, 84, 100, 117, 135, 154, 174, 195, 217, 240, 264, 289, 315, 342, 370, 399, 429, 460, 492, 525, 559, 594, 630, 667, 705, 744, 784, 825, more...

integer, non-monotonic, +-

a(n)=∑(n-8)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence o2bpwxsqvzqmg

-8, -7, -5, -2, 2, 7, 13, 20, 28, 37, 47, 58, 70, 83, 97, 112, 128, 145, 163, 182, 202, 223, 245, 268, 292, 317, 343, 370, 398, 427, 457, 488, 520, 553, 587, 622, 658, 695, 733, 772, 812, 853, 895, 938, 982, 1027, 1073, 1120, 1168, 1217, more...

integer, strictly-monotonic, +-

a(n)=∑(n)-8
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence qy4wnvnpgpbah

-7, -13, -18, -22, -25, -27, -28, -28, -27, -25, -22, -18, -13, -7, 0, 8, 17, 27, 38, 50, 63, 77, 92, 108, 125, 143, 162, 182, 203, 225, 248, 272, 297, 323, 350, 378, 407, 437, 468, 500, 533, 567, 602, 638, 675, 713, 752, 792, 833, 875, more...

integer, non-monotonic, +-

a(n)=∑(n-7)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence lypqgpr01l13

-7, -6, -4, -1, 3, 8, 14, 21, 29, 38, 48, 59, 71, 84, 98, 113, 129, 146, 164, 183, 203, 224, 246, 269, 293, 318, 344, 371, 399, 428, 458, 489, 521, 554, 588, 623, 659, 696, 734, 773, 813, 854, 896, 939, 983, 1028, 1074, 1121, 1169, 1218, more...

integer, strictly-monotonic, +-

a(n)=∑(n)-7
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence 4y1ctkcanpval

-6, -11, -15, -18, -20, -21, -21, -20, -18, -15, -11, -6, 0, 7, 15, 24, 34, 45, 57, 70, 84, 99, 115, 132, 150, 169, 189, 210, 232, 255, 279, 304, 330, 357, 385, 414, 444, 475, 507, 540, 574, 609, 645, 682, 720, 759, 799, 840, 882, 925, more...

integer, non-monotonic, +-

a(n)=∑(n-6)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence gab4022npuc3k

-6, -5, -3, 0, 4, 9, 15, 22, 30, 39, 49, 60, 72, 85, 99, 114, 130, 147, 165, 184, 204, 225, 247, 270, 294, 319, 345, 372, 400, 429, 459, 490, 522, 555, 589, 624, 660, 697, 735, 774, 814, 855, 897, 940, 984, 1029, 1075, 1122, 1170, 1219, more...

integer, strictly-monotonic, +-

a(n)=∑(n)-6
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence hsjs2pdiyk0dl

-5, -9, -12, -14, -15, -15, -14, -12, -9, -5, 0, 6, 13, 21, 30, 40, 51, 63, 76, 90, 105, 121, 138, 156, 175, 195, 216, 238, 261, 285, 310, 336, 363, 391, 420, 450, 481, 513, 546, 580, 615, 651, 688, 726, 765, 805, 846, 888, 931, 975, more...

integer, non-monotonic, +-

a(n)=∑(n-5)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=-∑(a(n-1)-1)
a(0)=5
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence gvwtlbs0hxihm

-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)=∑(n)-5
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence fswqre0odq03m

-4, -7, -9, -10, -10, -9, -7, -4, 0, 5, 11, 18, 26, 35, 45, 56, 68, 81, 95, 110, 126, 143, 161, 180, 200, 221, 243, 266, 290, 315, 341, 368, 396, 425, 455, 486, 518, 551, 585, 620, 656, 693, 731, 770, 810, 851, 893, 936, 980, 1025, more...

integer, non-monotonic, +-

a(n)=∑(n-4)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=-∑(a(n-1)-1)
a(0)=4
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence wiz3nw2rzgc3e

-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)=∑(n)-4
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence vxst0i323go3o

-3.1415926536, -5.2831853072, -6.4247779608, -6.5663706144, -5.7079632679, -3.8495559215, -0.9911485751, 2.8672587713, 7.7256661177, 13.5840734641, 20.4424808105, 28.3008881569, 37.1592955033, 47.0177028497, 57.8761101962, 69.7345175426, 82.592924889, 96.4513322354, 111.3097395818, 127.1681469282, 144.0265542746, 161.884961621, 180.7433689674, 200.6017763138, 221.4601836603, more...

decimal, non-monotonic, +-

a(n)=∑(n-π)
π=3.141...
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence 1gux1013g4cvc

-3.1415926536, -2.1415926536, -0.1415926536, 2.8584073464, 6.8584073464, 11.8584073464, 17.8584073464, 24.8584073464, 32.8584073464, 41.8584073464, 51.8584073464, 62.8584073464, 74.8584073464, 87.8584073464, 101.8584073464, 116.8584073464, 132.8584073464, 149.8584073464, 167.8584073464, 186.8584073464, 206.8584073464, 227.8584073464, 249.8584073464, 272.8584073464, 296.8584073464, more...

decimal, strictly-monotonic, +-

a(n)=∑(n)-π
∑(a)=partial sums of a
π=3.141...
n≥0
4 operations
Arithmetic

Sequence uekrfj3vojcy

-3, -5, -6, -6, -5, -3, 0, 4, 9, 15, 22, 30, 39, 49, 60, 72, 85, 99, 114, 130, 147, 165, 184, 204, 225, 247, 270, 294, 319, 345, 372, 400, 429, 459, 490, 522, 555, 589, 624, 660, 697, 735, 774, 814, 855, 897, 940, 984, 1029, 1075, more...

integer, non-monotonic, +-

a(n)=∑(n-3)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=-∑(a(n-1)-1)
a(0)=3
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence e0tgg14pfiwmp

-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)=∑(n)-3
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence kb3orp4c405sn

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

integer, non-monotonic, +-, A167544

a(n)=∑(n-2)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=-∑(a(n-1)-1)
a(0)=2
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence v3vkuw40xipti

-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)=∑(n)-2
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence ral3ikpq5phon

-1, -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, more...

integer, monotonic, +-

a(n)=∑(n-1)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=-∑(a(n-1)-1)
a(0)=1
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence ahcpequn050lm

-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)=∑(n)-1
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence 0r02t3allbm1c

0, 0.1, 0.3, 0.6, 1, 1.5, 2.1, 2.8, 3.6, 4.5, 5.5, 6.6, 7.8, 9.1, 10.5, 12, 13.6, 15.3, 17.1, 19, 21, 23.1, 25.3, 27.6, 30, more...

decimal, strictly-monotonic, +

a(n)=n/10+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(n/10)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence zuk4mafgnyckn

0, 0.1111111111, 0.3333333333, 0.6666666667, 1.1111111111, 1.6666666667, 2.3333333333, 3.1111111111, 4, 5, 6.1111111111, 7.3333333333, 8.6666666667, 10.1111111111, 11.6666666667, 13.3333333333, 15.1111111111, 17, 19, 21.1111111111, 23.3333333333, 25.6666666667, 28.1111111111, 30.6666666667, 33.3333333333, more...

decimal, strictly-monotonic, +

a(n)=n/9+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(n/9)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence vwe1giakvordj

0, 0.125, 0.375, 0.75, 1.25, 1.875, 2.625, 3.5, 4.5, 5.625, 6.875, 8.25, 9.75, 11.375, 13.125, 15, 17, 19.125, 21.375, 23.75, 26.25, 28.875, 31.625, 34.5, 37.5, more...

decimal, strictly-monotonic, +

a(n)=n/8+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(n/8)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence vkopigykd5nqf

0, 0.1428571429, 0.4285714286, 0.8571428571, 1.4285714286, 2.1428571429, 3, 4, 5.1428571429, 6.4285714286, 7.8571428571, 9.4285714286, 11.1428571429, 13, 15, 17.1428571429, 19.4285714286, 21.8571428571, 24.4285714286, 27.1428571429, 30, 33, 36.1428571429, 39.4285714286, 42.8571428571, more...

decimal, strictly-monotonic, +

a(n)=n/7+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(n/7)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence w4zy1aju55stc

0, 0.1666666667, 0.5, 1, 1.6666666667, 2.5, 3.5, 4.6666666667, 6, 7.5, 9.1666666667, 11, 13, 15.1666666667, 17.5, 20, 22.6666666667, 25.5, 28.5, 31.6666666667, 35, 38.5, 42.1666666667, 46, 50, more...

decimal, strictly-monotonic, +

a(n)=n/6+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(n/6)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence h143rak2gl0ce

0, 0.2, 0.6, 1.2, 2, 3, 4.2, 5.6, 7.2, 9, 11, 13.2, 15.6, 18.2, 21, 24, 27.2, 30.6, 34.2, 38, 42, 46.2, 50.6, 55.2, 60, more...

decimal, strictly-monotonic, +

a(n)=n/5+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(n/5)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence shwvfna0ogvd

0, 0.25, 0.75, 1.5, 2.5, 3.75, 5.25, 7, 9, 11.25, 13.75, 16.5, 19.5, 22.75, 26.25, 30, 34, 38.25, 42.75, 47.5, 52.5, 57.75, 63.25, 69, 75, more...

decimal, strictly-monotonic, +

a(n)=n/4+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(n/4)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence tajclfbi5desj

0, 0.3183098862, 0.9549296586, 1.9098593171, 3.1830988618, 4.7746482928, 6.6845076099, 8.9126768131, 11.4591559026, 14.3239448783, 17.5070437401, 21.0084524881, 24.8281711223, 28.9661996427, 33.4225380493, 38.1971863421, 43.290144521, 48.7014125861, 54.4309905374, 60.4788783749, 66.8450760986, 73.5295837085, 80.5324012045, 87.8535285867, 95.4929658551, more...

decimal, strictly-monotonic, +

a(n)=n/π+a(n-1)
a(0)=0
π=3.141...
n≥0
5 operations
Recursive
a(n)=∑(n/π)
π=3.141...
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence exxcim4pcj3vj

0, 0.3333333333, 1, 2, 3.3333333333, 5, 7, 9.3333333333, 12, 15, 18.3333333333, 22, 26, 30.3333333333, 35, 40, 45.3333333333, 51, 57, 63.3333333333, 70, 77, 84.3333333333, 92, 100, more...

decimal, strictly-monotonic, +

a(n)=n/3+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(n/3)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence z2mb2oag0by5b

0, 0.5, 1.5, 3, 5, 7.5, 10.5, 14, 18, 22.5, 27.5, 33, 39, 45.5, 52.5, 60, 68, 76.5, 85.5, 95, 105, 115.5, 126.5, 138, 150, more...

decimal, strictly-monotonic, +

a(n)=∑(n/2)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=n/2+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(log(sqrt(exp(n))))
∑(a)=partial sums of a
n≥0
5 operations
Power

Sequence hkdawpl1vmhoe

0, 3, 9, 18, 30, 45, 63, 84, 108, 135, 165, 198, 234, 273, 315, 360, 408, 459, 513, 570, 630, 693, 759, 828, 900, 975, 1053, 1134, 1218, 1305, 1395, 1488, 1584, 1683, 1785, 1890, 1998, 2109, 2223, 2340, 2460, 2583, 2709, 2838, 2970, 3105, 3243, 3384, 3528, 3675, more...

integer, strictly-monotonic, +, A045943

a(n)=3*n+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(3*n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence 4q5f155ooprpg

0, 3.1415926536, 9.4247779608, 18.8495559215, 31.4159265359, 47.1238898038, 65.9734457254, 87.9645943005, 113.0973355292, 141.3716694115, 172.7875959474, 207.3451151369, 245.04422698, 285.8849314767, 329.8672286269, 376.9911184308, 427.2566008882, 480.6636759992, 537.2123437639, 596.9026041821, 659.7344572539, 725.7079029792, 794.8229413582, 867.0795723908, 942.4777960769, more...

decimal, strictly-monotonic, +

a(n)=π*n+a(n-1)
a(0)=0
π=3.141...
n≥0
5 operations
Recursive
a(n)=∑(π*n)
π=3.141...
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence ysvzf1qoeah4l

0, 4, 12, 24, 40, 60, 84, 112, 144, 180, 220, 264, 312, 364, 420, 480, 544, 612, 684, 760, 840, 924, 1012, 1104, 1200, 1300, 1404, 1512, 1624, 1740, 1860, 1984, 2112, 2244, 2380, 2520, 2664, 2812, 2964, 3120, 3280, 3444, 3612, 3784, 3960, 4140, 4324, 4512, 4704, 4900, more...

integer, strictly-monotonic, +, A046092

a(n)=∑(4*n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=4*n+a(n-1)
a(0)=0
n≥0
5 operations
Recursive

Sequence ni2h1dap5sy1n

0, 5, 15, 30, 50, 75, 105, 140, 180, 225, 275, 330, 390, 455, 525, 600, 680, 765, 855, 950, 1050, 1155, 1265, 1380, 1500, 1625, 1755, 1890, 2030, 2175, 2325, 2480, 2640, 2805, 2975, 3150, 3330, 3515, 3705, 3900, 4100, 4305, 4515, 4730, 4950, 5175, 5405, 5640, 5880, 6125, more...

integer, strictly-monotonic, +, A028895

a(n)=5*n+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(5*n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence r2d5jn0hm4tzb

0, 6, 18, 36, 60, 90, 126, 168, 216, 270, 330, 396, 468, 546, 630, 720, 816, 918, 1026, 1140, 1260, 1386, 1518, 1656, 1800, 1950, 2106, 2268, 2436, 2610, 2790, 2976, 3168, 3366, 3570, 3780, 3996, 4218, 4446, 4680, 4920, 5166, 5418, 5676, 5940, 6210, 6486, 6768, 7056, 7350, more...

integer, strictly-monotonic, +, A028896

a(n)=6*n+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(6*n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence m2qau4nl1k3wm

0, 7, 21, 42, 70, 105, 147, 196, 252, 315, 385, 462, 546, 637, 735, 840, 952, 1071, 1197, 1330, 1470, 1617, 1771, 1932, 2100, 2275, 2457, 2646, 2842, 3045, 3255, 3472, 3696, 3927, 4165, 4410, 4662, 4921, 5187, 5460, 5740, 6027, 6321, 6622, 6930, 7245, 7567, 7896, 8232, 8575, more...

integer, strictly-monotonic, +, A024966

a(n)=7*n+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(7*n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence e3od0sa0wkau

0, 8, 24, 48, 80, 120, 168, 224, 288, 360, 440, 528, 624, 728, 840, 960, 1088, 1224, 1368, 1520, 1680, 1848, 2024, 2208, 2400, 2600, 2808, 3024, 3248, 3480, 3720, 3968, 4224, 4488, 4760, 5040, 5328, 5624, 5928, 6240, 6560, 6888, 7224, 7568, 7920, 8280, 8648, 9024, 9408, 9800, more...

integer, strictly-monotonic, +, A033996

a(n)=8*n+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(8*n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence n4eo1pw0jkbyf

0, 9, 27, 54, 90, 135, 189, 252, 324, 405, 495, 594, 702, 819, 945, 1080, 1224, 1377, 1539, 1710, 1890, 2079, 2277, 2484, 2700, 2925, 3159, 3402, 3654, 3915, 4185, 4464, 4752, 5049, 5355, 5670, 5994, 6327, 6669, 7020, 7380, 7749, 8127, 8514, 8910, 9315, 9729, 10152, 10584, 11025, more...

integer, strictly-monotonic, +, A027468

a(n)=∑(9*n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=9*n+a(n-1)
a(0)=0
n≥0
5 operations
Recursive

Sequence djwxobrrjib5d

0, 10, 30, 60, 100, 150, 210, 280, 360, 450, 550, 660, 780, 910, 1050, 1200, 1360, 1530, 1710, 1900, 2100, 2310, 2530, 2760, 3000, 3250, 3510, 3780, 4060, 4350, 4650, 4960, 5280, 5610, 5950, 6300, 6660, 7030, 7410, 7800, 8200, 8610, 9030, 9460, 9900, 10350, 10810, 11280, 11760, 12250, more...

integer, strictly-monotonic, +, A124080

a(n)=10*n+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(10*n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence bdlfffctzinbm

1, 0.3333333333, 0.1666666667, 0.1, 0.0666666667, 0.0476190476, 0.0357142857, 0.0277777778, 0.0222222222, 0.0181818182, 0.0151515152, 0.0128205128, 0.010989011, 0.0095238095, 0.0083333333, 0.0073529412, 0.0065359477, 0.0058479532, 0.0052631579, 0.0047619048, 0.0043290043, 0.0039525692, 0.0036231884, 0.0033333333, 0.0030769231, more...

decimal, strictly-monotonic, +

a(n)=1/∑(n)
∑(a)=partial sums of a
n≥1
4 operations
Arithmetic
a(n)=a(n-1)/(1+2/n)
a(0)=1
n≥0
7 operations
Recursive
a(n)=exp(-log(∑(n)))
∑(a)=partial sums of a
n≥1
5 operations
Power

Sequence tddayd2lhcryl

1, 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, more...

integer, monotonic, +-, A080956

a(n)=∑(1-n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=1-n+a(n-1)
a(0)=1
n≥0
5 operations
Recursive
a(n)=(1-n)%n+a(n-1)
a(0)=1
n≥0
7 operations
Divisibility

Sequence ujgsbuzks4lbj

1, 1.5, 1.8333333333, 2.0833333333, 2.2833333333, 2.45, 2.5928571429, 2.7178571429, 2.828968254, 2.928968254, 3.0198773449, 3.1032106782, 3.1801337551, 3.2515623266, 3.3182289932, 3.3807289932, 3.4395525226, 3.4951080782, 3.5477396571, 3.5977396571, 3.6453587048, 3.6908132502, 3.7342915111, 3.7759581778, 3.8159581778, more...

decimal, strictly-monotonic, +

a(n)=∑(1/n)
∑(a)=partial sums of a
n≥1
4 operations
Arithmetic
a(n)=1/(1+n)+a(n-1)
a(0)=1
n≥0
7 operations
Recursive
a(n)=∑(n^-1)
∑(a)=partial sums of a
n≥1
5 operations
Power

Sequence z5yvl43ezd5vo

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, 1275, more...

integer, strictly-monotonic, +

a(n)=∑(1+n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=1+n+a(n-1)
a(0)=1
n≥0
5 operations
Recursive
a(n)=C(2+n, 2)
C(n,k)=binomial coefficient
n≥0
5 operations
Combinatoric
a(n)=Δ(∑(∑(n)))
∑(a)=partial sums of a
Δ(a)=differences of a
n≥0
4 operations
Variable
a(n)=∑(lcm(n, gpf(n)))
gpf(n)=greatest prime factor of n
lcm(a,b)=least common multiple
∑(a)=partial sums of a
n≥1
5 operations
Prime
a(n)=exp(abs(log(∑(n))))
∑(a)=partial sums of a
n≥1
5 operations
Power

Sequence ngupxftw4ibtp

2, 0.6666666667, 0.3333333333, 0.2, 0.1333333333, 0.0952380952, 0.0714285714, 0.0555555556, 0.0444444444, 0.0363636364, 0.0303030303, 0.0256410256, 0.021978022, 0.019047619, 0.0166666667, 0.0147058824, 0.0130718954, 0.0116959064, 0.0105263158, 0.0095238095, 0.0086580087, 0.0079051383, 0.0072463768, 0.0066666667, 0.0061538462, more...

decimal, strictly-monotonic, +

a(n)=2/∑(n)
∑(a)=partial sums of a
n≥1
4 operations
Arithmetic
a(n)=n/((2+n)/a(n-1))
a(0)=2
n≥0
7 operations
Recursive

Sequence thsvbvvnd555b

2, 3, 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, more...

integer, non-monotonic, +-

a(n)=∑(2-n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=2-n+a(n-1)
a(0)=2
n≥0
5 operations
Recursive

Sequence copfc3asqk3fe

2, 3, 3.6666666667, 4.1666666667, 4.5666666667, 4.9, 5.1857142857, 5.4357142857, 5.6579365079, 5.8579365079, 6.0397546898, 6.2064213564, 6.3602675103, 6.5031246531, 6.6364579865, 6.7614579865, 6.8791050453, 6.9902161564, 7.0954793143, 7.1954793143, 7.2907174095, 7.3816265004, 7.4685830222, 7.5519163555, 7.6319163555, more...

decimal, strictly-monotonic, +

a(n)=∑(2/n)
∑(a)=partial sums of a
n≥1
4 operations
Arithmetic

Sequence jpcy12ciyc4ei

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, 1274, 1325, more...

integer, strictly-monotonic, +

a(n)=∑(2+n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=∑(1+a(n-1))
a(0)=2
∑(a)=partial sums of a
n≥0
4 operations
Recursive
a(n)=2+n%a(n-1)+a(n-1)
a(0)=2
n≥0
7 operations
Divisibility
a(n)=∑(floor(∑(sqrt(a(n-1)))))
a(0)=2
∑(a)=partial sums of a
n≥0
5 operations
Power

Sequence 1ddwihpidl5ee

3, 1, 0.5, 0.3, 0.2, 0.1428571429, 0.1071428571, 0.0833333333, 0.0666666667, 0.0545454545, 0.0454545455, 0.0384615385, 0.032967033, 0.0285714286, 0.025, 0.0220588235, 0.0196078431, 0.0175438596, 0.0157894737, 0.0142857143, 0.012987013, 0.0118577075, 0.0108695652, 0.01, 0.0092307692, more...

decimal, strictly-monotonic, +

a(n)=3/∑(n)
∑(a)=partial sums of a
n≥1
4 operations
Arithmetic

Sequence 51w5ohpno01nc

3, 4.5, 5.5, 6.25, 6.85, 7.35, 7.7785714286, 8.1535714286, 8.4869047619, 8.7869047619, 9.0596320346, 9.3096320346, 9.5404012654, 9.7546869797, 9.9546869797, 10.1421869797, 10.3186575679, 10.4853242346, 10.6432189714, 10.7932189714, 10.9360761143, 11.0724397507, 11.2028745333, 11.3278745333, 11.4478745333, more...

decimal, strictly-monotonic, +

a(n)=∑(3/n)
∑(a)=partial sums of a
n≥1
4 operations
Arithmetic

Sequence 3gkdi5eirsx2d

3, 5, 6, 6, 5, 3, 0, -4, -9, -15, -22, -30, -39, -49, -60, -72, -85, -99, -114, -130, -147, -165, -184, -204, -225, -247, -270, -294, -319, -345, -372, -400, -429, -459, -490, -522, -555, -589, -624, -660, -697, -735, -774, -814, -855, -897, -940, -984, -1029, -1075, more...

integer, non-monotonic, +-

a(n)=∑(3-n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=3-n+a(n-1)
a(0)=3
n≥0
5 operations
Recursive

Sequence iz4xnal1ntfmo

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, 1272, 1323, 1375, more...

integer, strictly-monotonic, +

a(n)=∑(1+a(n-1))
a(0)=3
∑(a)=partial sums of a
n≥0
4 operations
Recursive
a(n)=∑(3+n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence aws3n1whsgbdg

3.1415926536, 1.0471975512, 0.5235987756, 0.3141592654, 0.2094395102, 0.1495996502, 0.1121997376, 0.0872664626, 0.0698131701, 0.0571198664, 0.0475998887, 0.0402768289, 0.0345229962, 0.02991993, 0.0261799388, 0.023099946, 0.0205332853, 0.0183718869, 0.0165346982, 0.014959965, 0.0135999682, 0.0124173623, 0.0113825821, 0.0104719755, 0.0096664389, more...

decimal, strictly-monotonic, +

a(n)=π/∑(n)
π=3.141...
∑(a)=partial sums of a
n≥1
4 operations
Arithmetic

Sequence 3x12yznb1iztf

3.1415926536, 2.1415926536, 0.1415926536, -2.8584073464, -6.8584073464, -11.8584073464, -17.8584073464, -24.8584073464, -32.8584073464, -41.8584073464, -51.8584073464, -62.8584073464, -74.8584073464, -87.8584073464, -101.8584073464, -116.8584073464, -132.8584073464, -149.8584073464, -167.8584073464, -186.8584073464, -206.8584073464, -227.8584073464, -249.8584073464, -272.8584073464, -296.8584073464, more...

decimal, strictly-monotonic, +-

a(n)=π-∑(n)
π=3.141...
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence dsycr0nhbgruc

3.1415926536, 4.1415926536, 6.1415926536, 9.1415926536, 13.1415926536, 18.1415926536, 24.1415926536, 31.1415926536, 39.1415926536, 48.1415926536, 58.1415926536, 69.1415926536, 81.1415926536, 94.1415926536, 108.1415926536, 123.1415926536, 139.1415926536, 156.1415926536, 174.1415926536, 193.1415926536, 213.1415926536, 234.1415926536, 256.1415926536, 279.1415926536, 303.1415926536, more...

decimal, strictly-monotonic, +

a(n)=π+∑(n)
π=3.141...
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence kl4cw2zop20eh

3.1415926536, 4.7123889804, 5.7595865316, 6.544984695, 7.1733032257, 7.6969020013, 8.1457009518, 8.5384000335, 8.8874658839, 9.2016251493, 9.4872244814, 9.7490238692, 9.9906848426, 10.2150843178, 10.4245238281, 10.6208733689, 10.8056729368, 10.980205862, 11.1455528437, 11.3026324764, 11.4522321266, 11.5950317927, 11.7316227776, 11.8625224715, 11.9881861776, more...

decimal, strictly-monotonic, +

a(n)=∑(π/n)
π=3.141...
∑(a)=partial sums of a
n≥1
4 operations
Arithmetic

Sequence ovbbkl4keej5

3.1415926536, 5.2831853072, 6.4247779608, 6.5663706144, 5.7079632679, 3.8495559215, 0.9911485751, -2.8672587713, -7.7256661177, -13.5840734641, -20.4424808105, -28.3008881569, -37.1592955033, -47.0177028497, -57.8761101962, -69.7345175426, -82.592924889, -96.4513322354, -111.3097395818, -127.1681469282, -144.0265542746, -161.884961621, -180.7433689674, -200.6017763138, -221.4601836603, more...

decimal, non-monotonic, +-

a(n)=∑(π-n)
π=3.141...
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence gosz0lqvt3l0o

3.1415926536, 7.2831853072, 12.4247779608, 18.5663706144, 25.7079632679, 33.8495559215, 42.9911485751, 53.1327412287, 64.2743338823, 76.4159265359, 89.5575191895, 103.6991118431, 118.8407044967, 134.9822971503, 152.1238898038, 170.2654824574, 189.407075111, 209.5486677646, 230.6902604182, 252.8318530718, 275.9734457254, 300.115038379, 325.2566310326, 351.3982236862, 378.5398163397, more...

decimal, strictly-monotonic, +

a(n)=∑(π+n)
π=3.141...
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence z5xutqbr0uyol

4, 1.3333333333, 0.6666666667, 0.4, 0.2666666667, 0.1904761905, 0.1428571429, 0.1111111111, 0.0888888889, 0.0727272727, 0.0606060606, 0.0512820513, 0.043956044, 0.0380952381, 0.0333333333, 0.0294117647, 0.0261437908, 0.0233918129, 0.0210526316, 0.019047619, 0.0173160173, 0.0158102767, 0.0144927536, 0.0133333333, 0.0123076923, more...

decimal, strictly-monotonic, +

a(n)=4/∑(n)
∑(a)=partial sums of a
n≥1
4 operations
Arithmetic

Sequence ctm1nast0iimp

4, 6, 7.3333333333, 8.3333333333, 9.1333333333, 9.8, 10.3714285714, 10.8714285714, 11.3158730159, 11.7158730159, 12.0795093795, 12.4128427128, 12.7205350205, 13.0062493062, 13.2729159729, 13.5229159729, 13.7582100906, 13.9804323128, 14.1909586286, 14.3909586286, 14.5814348191, 14.7632530009, 14.9371660443, 15.103832711, 15.263832711, more...

decimal, strictly-monotonic, +

a(n)=∑(4/n)
∑(a)=partial sums of a
n≥1
4 operations
Arithmetic

Sequence zvvs01dr2xrxc

4, 7, 9, 10, 10, 9, 7, 4, 0, -5, -11, -18, -26, -35, -45, -56, -68, -81, -95, -110, -126, -143, -161, -180, -200, -221, -243, -266, -290, -315, -341, -368, -396, -425, -455, -486, -518, -551, -585, -620, -656, -693, -731, -770, -810, -851, -893, -936, -980, -1025, more...

integer, non-monotonic, +-

a(n)=∑(4-n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=4-n+a(n-1)
a(0)=4
n≥0
5 operations
Recursive

Sequence mnxzqxqprzztd

4, 9, 15, 22, 30, 39, 49, 60, 72, 85, 99, 114, 130, 147, 165, 184, 204, 225, 247, 270, 294, 319, 345, 372, 400, 429, 459, 490, 522, 555, 589, 624, 660, 697, 735, 774, 814, 855, 897, 940, 984, 1029, 1075, 1122, 1170, 1219, 1269, 1320, 1372, 1425, more...

integer, strictly-monotonic, +

a(n)=∑(1+a(n-1))
a(0)=4
∑(a)=partial sums of a
n≥0
4 operations
Recursive
a(n)=∑(4+n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence xrdkqavgcjde

5, 1.6666666667, 0.8333333333, 0.5, 0.3333333333, 0.2380952381, 0.1785714286, 0.1388888889, 0.1111111111, 0.0909090909, 0.0757575758, 0.0641025641, 0.0549450549, 0.0476190476, 0.0416666667, 0.0367647059, 0.0326797386, 0.0292397661, 0.0263157895, 0.0238095238, 0.0216450216, 0.0197628458, 0.018115942, 0.0166666667, 0.0153846154, more...

decimal, strictly-monotonic, +

a(n)=5/∑(n)
∑(a)=partial sums of a
n≥1
4 operations
Arithmetic

Sequence karldjmo1m2yp

5, 7.5, 9.1666666667, 10.4166666667, 11.4166666667, 12.25, 12.9642857143, 13.5892857143, 14.1448412698, 14.6448412698, 15.0993867244, 15.5160533911, 15.9006687757, 16.2578116328, 16.5911449661, 16.9036449661, 17.1977626132, 17.475540391, 17.7386982857, 17.9886982857, 18.2267935238, 18.4540662511, 18.6714575554, 18.8797908888, 19.0797908888, more...

decimal, strictly-monotonic, +

a(n)=∑(5/n)
∑(a)=partial sums of a
n≥1
4 operations
Arithmetic

Sequence gy05pf3iildmj

5, 9, 12, 14, 15, 15, 14, 12, 9, 5, 0, -6, -13, -21, -30, -40, -51, -63, -76, -90, -105, -121, -138, -156, -175, -195, -216, -238, -261, -285, -310, -336, -363, -391, -420, -450, -481, -513, -546, -580, -615, -651, -688, -726, -765, -805, -846, -888, -931, -975, more...

integer, non-monotonic, +-

a(n)=∑(5-n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=5-n+a(n-1)
a(0)=5
n≥0
5 operations
Recursive

Sequence e5irpgby4c0qk

5, 11, 18, 26, 35, 45, 56, 68, 81, 95, 110, 126, 143, 161, 180, 200, 221, 243, 266, 290, 315, 341, 368, 396, 425, 455, 486, 518, 551, 585, 620, 656, 693, 731, 770, 810, 851, 893, 936, 980, 1025, 1071, 1118, 1166, 1215, 1265, 1316, 1368, 1421, 1475, more...

integer, strictly-monotonic, +

a(n)=∑(1+a(n-1))
a(0)=5
∑(a)=partial sums of a
n≥0
4 operations
Recursive
a(n)=∑(5+n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence ijmpsuvhpjc1i

6, 2, 1, 0.6, 0.4, 0.2857142857, 0.2142857143, 0.1666666667, 0.1333333333, 0.1090909091, 0.0909090909, 0.0769230769, 0.0659340659, 0.0571428571, 0.05, 0.0441176471, 0.0392156863, 0.0350877193, 0.0315789474, 0.0285714286, 0.025974026, 0.023715415, 0.0217391304, 0.02, 0.0184615385, more...

decimal, strictly-monotonic, +

a(n)=6/∑(n)
∑(a)=partial sums of a
n≥1
4 operations
Arithmetic

Sequence wjd4uukuxrbnj

6, 5, 3, 0, -4, -9, -15, -22, -30, -39, -49, -60, -72, -85, -99, -114, -130, -147, -165, -184, -204, -225, -247, -270, -294, -319, -345, -372, -400, -429, -459, -490, -522, -555, -589, -624, -660, -697, -735, -774, -814, -855, -897, -940, -984, -1029, -1075, -1122, -1170, -1219, more...

integer, strictly-monotonic, +-

a(n)=6-∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence jevepv23fn0eg

6, 7, 9, 12, 16, 21, 27, 34, 42, 51, 61, 72, 84, 97, 111, 126, 142, 159, 177, 196, 216, 237, 259, 282, 306, 331, 357, 384, 412, 441, 471, 502, 534, 567, 601, 636, 672, 709, 747, 786, 826, 867, 909, 952, 996, 1041, 1087, 1134, 1182, 1231, more...

integer, strictly-monotonic, +

a(n)=6+∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence urmwhtlqlgt4p

6, 9, 11, 12.5, 13.7, 14.7, 15.5571428571, 16.3071428571, 16.9738095238, 17.5738095238, 18.1192640693, 18.6192640693, 19.0808025308, 19.5093739594, 19.9093739594, 20.2843739594, 20.6373151358, 20.9706484692, 21.2864379429, 21.5864379429, 21.8721522286, 22.1448795013, 22.4057490665, 22.6557490665, 22.8957490665, more...

decimal, strictly-monotonic, +

a(n)=∑(6/n)
∑(a)=partial sums of a
n≥1
4 operations
Arithmetic

Sequence n0owqtmjngao

6, 11, 15, 18, 20, 21, 21, 20, 18, 15, 11, 6, 0, -7, -15, -24, -34, -45, -57, -70, -84, -99, -115, -132, -150, -169, -189, -210, -232, -255, -279, -304, -330, -357, -385, -414, -444, -475, -507, -540, -574, -609, -645, -682, -720, -759, -799, -840, -882, -925, more...

integer, non-monotonic, +-

a(n)=∑(6-n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence nwocr3mupvede

6, 13, 21, 30, 40, 51, 63, 76, 90, 105, 121, 138, 156, 175, 195, 216, 238, 261, 285, 310, 336, 363, 391, 420, 450, 481, 513, 546, 580, 615, 651, 688, 726, 765, 805, 846, 888, 931, 975, 1020, 1066, 1113, 1161, 1210, 1260, 1311, 1363, 1416, 1470, 1525, more...

integer, strictly-monotonic, +

a(n)=∑(6+n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence ifcozs0bt5f0g

7, 2.3333333333, 1.1666666667, 0.7, 0.4666666667, 0.3333333333, 0.25, 0.1944444444, 0.1555555556, 0.1272727273, 0.1060606061, 0.0897435897, 0.0769230769, 0.0666666667, 0.0583333333, 0.0514705882, 0.045751634, 0.0409356725, 0.0368421053, 0.0333333333, 0.0303030303, 0.0276679842, 0.0253623188, 0.0233333333, 0.0215384615, more...

decimal, strictly-monotonic, +

a(n)=7/∑(n)
∑(a)=partial sums of a
n≥1
4 operations
Arithmetic

Sequence nasfyn3vfppfk

7, 6, 4, 1, -3, -8, -14, -21, -29, -38, -48, -59, -71, -84, -98, -113, -129, -146, -164, -183, -203, -224, -246, -269, -293, -318, -344, -371, -399, -428, -458, -489, -521, -554, -588, -623, -659, -696, -734, -773, -813, -854, -896, -939, -983, -1028, -1074, -1121, -1169, -1218, more...

integer, strictly-monotonic, +-

a(n)=7-∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence vc3k5vodjggul

7, 8, 10, 13, 17, 22, 28, 35, 43, 52, 62, 73, 85, 98, 112, 127, 143, 160, 178, 197, 217, 238, 260, 283, 307, 332, 358, 385, 413, 442, 472, 503, 535, 568, 602, 637, 673, 710, 748, 787, 827, 868, 910, 953, 997, 1042, 1088, 1135, 1183, 1232, more...

integer, strictly-monotonic, +

a(n)=7+∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence 0uuf0g4otlhfp

7, 10.5, 12.8333333333, 14.5833333333, 15.9833333333, 17.15, 18.15, 19.025, 19.8027777778, 20.5027777778, 21.1391414141, 21.7224747475, 22.2609362859, 22.7609362859, 23.2276029526, 23.6651029526, 24.0768676585, 24.4657565474, 24.8341776, 25.1841776, 25.5175109333, 25.8356927515, 26.1400405776, 26.4317072443, 26.7117072443, more...

decimal, strictly-monotonic, +

a(n)=∑(7/n)
∑(a)=partial sums of a
n≥1
4 operations
Arithmetic

Sequence nxljwp44csp2d

7, 13, 18, 22, 25, 27, 28, 28, 27, 25, 22, 18, 13, 7, 0, -8, -17, -27, -38, -50, -63, -77, -92, -108, -125, -143, -162, -182, -203, -225, -248, -272, -297, -323, -350, -378, -407, -437, -468, -500, -533, -567, -602, -638, -675, -713, -752, -792, -833, -875, more...

integer, non-monotonic, +-

a(n)=∑(7-n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence txesdqkhr5pb

7, 15, 24, 34, 45, 57, 70, 84, 99, 115, 132, 150, 169, 189, 210, 232, 255, 279, 304, 330, 357, 385, 414, 444, 475, 507, 540, 574, 609, 645, 682, 720, 759, 799, 840, 882, 925, 969, 1014, 1060, 1107, 1155, 1204, 1254, 1305, 1357, 1410, 1464, 1519, 1575, more...

integer, strictly-monotonic, +

a(n)=∑(7+n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence fhbkn4ytftle

8, 2.6666666667, 1.3333333333, 0.8, 0.5333333333, 0.380952381, 0.2857142857, 0.2222222222, 0.1777777778, 0.1454545455, 0.1212121212, 0.1025641026, 0.0879120879, 0.0761904762, 0.0666666667, 0.0588235294, 0.0522875817, 0.0467836257, 0.0421052632, 0.0380952381, 0.0346320346, 0.0316205534, 0.0289855072, 0.0266666667, 0.0246153846, more...

decimal, strictly-monotonic, +

a(n)=8/∑(n)
∑(a)=partial sums of a
n≥1
4 operations
Arithmetic

Sequence g1opbshuxhw1l

8, 7, 5, 2, -2, -7, -13, -20, -28, -37, -47, -58, -70, -83, -97, -112, -128, -145, -163, -182, -202, -223, -245, -268, -292, -317, -343, -370, -398, -427, -457, -488, -520, -553, -587, -622, -658, -695, -733, -772, -812, -853, -895, -938, -982, -1027, -1073, -1120, -1168, -1217, more...

integer, strictly-monotonic, +-

a(n)=8-∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence pdvnfz24b2go

8, 9, 11, 14, 18, 23, 29, 36, 44, 53, 63, 74, 86, 99, 113, 128, 144, 161, 179, 198, 218, 239, 261, 284, 308, 333, 359, 386, 414, 443, 473, 504, 536, 569, 603, 638, 674, 711, 749, 788, 828, 869, 911, 954, 998, 1043, 1089, 1136, 1184, 1233, more...

integer, strictly-monotonic, +

a(n)=8+∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence 3qfuvpzlyz0kd

8, 12, 14.6666666667, 16.6666666667, 18.2666666667, 19.6, 20.7428571429, 21.7428571429, 22.6317460317, 23.4317460317, 24.159018759, 24.8256854257, 25.4410700411, 26.0124986125, 26.5458319458, 27.0458319458, 27.5164201811, 27.9608646256, 28.3819172571, 28.7819172571, 29.1628696381, 29.5265060017, 29.8743320887, 30.207665422, 30.527665422, more...

decimal, strictly-monotonic, +

a(n)=∑(8/n)
∑(a)=partial sums of a
n≥1
4 operations
Arithmetic

Sequence zo21xawuz0uum

8, 15, 21, 26, 30, 33, 35, 36, 36, 35, 33, 30, 26, 21, 15, 8, 0, -9, -19, -30, -42, -55, -69, -84, -100, -117, -135, -154, -174, -195, -217, -240, -264, -289, -315, -342, -370, -399, -429, -460, -492, -525, -559, -594, -630, -667, -705, -744, -784, -825, more...

integer, non-monotonic, +-

a(n)=∑(8-n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

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