cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A118026 a(0) = 0, a(n) = a(n-1) + (largest integer which is <= n and is missing from the earlier terms of the sequence).

Original entry on oeis.org

0, 1, 3, 5, 9, 13, 19, 26, 34, 42, 52, 63, 75, 87, 101, 116, 132, 149, 167, 185, 205, 226, 248, 271, 295, 320, 345, 372, 400, 429, 459, 490, 522, 555, 588, 623, 659, 696, 734, 773, 813, 854, 895, 938, 982, 1027, 1073, 1120, 1168, 1217, 1267, 1318, 1369, 1422
Offset: 0

Views

Author

Leroy Quet, Apr 10 2006

Keywords

Links

Crossrefs

Cf. A118027, A118028, A118029, A118030, A094589.

Programs

  • Mathematica
    a = {1}; Do[AppendTo[a, a[[i - 1]] + SelectFirst[Reverse@ Range[i], FreeQ[a, #] &]], {i, 2, 53}]; {0}~Join~a (* Michael De Vlieger, Sep 16 2017 *)

Extensions

More terms from Sheedeh Dorri (spd145(AT)psu.edu) and Melissa Donovan (msd181(AT)psu.edu), Apr 18 2006

A118027 a(0) = 0, a(n) = a(n-1) + (smallest integer which is >= n and is missing from the earlier terms of the sequence).

Original entry on oeis.org

0, 1, 3, 7, 11, 16, 22, 30, 38, 47, 57, 69, 81, 94, 108, 123, 140, 157, 175, 194, 214, 235, 258, 281, 305, 330, 356, 383, 411, 440, 471, 502, 534, 567, 601, 636, 672, 709, 748, 787, 827, 868, 910, 953, 997, 1042, 1088, 1136, 1184, 1233, 1283, 1334, 1386, 1439
Offset: 0

Views

Author

Leroy Quet, Apr 10 2006

Keywords

Links

Crossrefs

Cf. A118026, A118028, A118029, A118030, A094589.

Programs

  • Mathematica
    a = {1}; Do[k = i; While[MemberQ[a, k], k++]; AppendTo[a, a[[i - 1]] + k], {i, 2, 53}]; {0}~Join~a (* Michael De Vlieger, Sep 16 2017 *)

Extensions

More terms from Wendy Kalasky (wkk107(AT)psu.edu), Apr 26 2006

A118029 a(0)=1. a(n) = a(n-1) + (smallest integer that is >= n and occurs among the earlier terms of the sequence).

Original entry on oeis.org

1, 2, 4, 8, 12, 20, 28, 36, 44, 56, 68, 80, 92, 112, 132, 152, 172, 192, 212, 232, 252, 280, 308, 336, 364, 392, 420, 448, 476, 512, 548, 584, 620, 656, 692, 728, 764, 808, 852, 896, 940, 984, 1028, 1072, 1116, 1172, 1228, 1284, 1340, 1396, 1452, 1508, 1564
Offset: 0

Views

Author

Leroy Quet, Apr 10 2006

Keywords

Comments

Let b_j(n) = 2*n*(n/2)^(2^(-j))/(1+2^(-j)). For any positive integers r and n, we have (n^2+n)/2 < a(n) < b_r(n) + Sum_{j=1..r} b_j(n). - Colin Defant, Sep 15 2015

Links

Crossrefs

Cf. A118026, A118027, A118028, A118030, A094589.

Programs

  • Mathematica
    a = {1}; Do[k = 1; While[Nand[MemberQ[a, k], k >= i], k++]; AppendTo[a, a[[i]] + k], {i, 52}]; a (* Michael De Vlieger, Sep 19 2017 *)
  • PARI
    lista(nn) = {va = vector(nn); va[1] = 1; for (k=2, nn, vs = select(x->(x >= k-1), va, 1); va[k] = va[k-1] + va[vs[1]];); va;} \\ Michel Marcus, Oct 09 2015

Extensions

More terms from Adam Panagos (adam.panagos(AT)gmail.com), May 10 2006
More terms from Joshua Zucker, Jul 27 2006

A118030 a(1)=1. a(n) = a(n-1) + (largest integer which is <= n and occurs among the earlier terms of the sequence).

Original entry on oeis.org

1, 2, 4, 8, 12, 16, 20, 28, 36, 44, 52, 64, 76, 88, 100, 116, 132, 148, 164, 184, 204, 224, 244, 264, 284, 304, 324, 352, 380, 408, 436, 464, 492, 520, 548, 584, 620, 656, 692, 728, 764, 800, 836, 880, 924, 968, 1012, 1056, 1100, 1144, 1188, 1240, 1292, 1344, 1396, 1448, 1500, 1552, 1604, 1656, 1708, 1760
Offset: 1

Views

Author

Leroy Quet, Apr 10 2006

Keywords

Links

Crossrefs

Cf. A118026, A118027, A118028, A118029, A094589.

Programs

  • Mathematica
    a = {1}; Do[k = i + 1; While[Nand[MemberQ[a, k], k <= i + 1], k--]; AppendTo[a, a[[i]] + k], {i, 61}]; a (* Michael De Vlieger, Sep 19 2017 *)

Extensions

More terms from Melissa Donovan (msd181(AT)psu.edu), Apr 23 2006
Showing 1-4 of 4 results.

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