A094589 -id:A094589 - cp's OEIS frontend

A250983 First differences of A094589.

1, 2, 2, 4, 4, 6, 6, 6, 6, 10, 10, 10, 10, 14, 14, 14, 14, 14, 14, 20, 20, 20, 20, 20, 20, 26, 26, 26, 26, 26, 26, 32, 32, 32, 32, 32, 32, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58

Offset: 1

Ivan Neretin, Mar 20 2015

Also, a Golomb-type sequence over A094589, i.e., a sequence obtained from A094589 by repeating each term a certain number of times so that the succession of run lengths of the resulting sequence is again that same sequence.

Has the property of idempotence: a(a(n))=a(n).

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A094589 (a(n) with repetitions removed), A001462 (Golomb's sequence), A013189 (Golomb's sequence over squares).

w = {1, 2, 2};
i = 3;
Do[
  w = Join[w, Array[Length[w] + 1 &, w[[i++]]]];
  , {n, 10}
  ];
w

flargest(va, n) = {vsa = vecsort(va,,12); for (k=1, #vsa, if (vsa[k] < n, return (vsa[k])););}
lista(nn) = {voa = [1]; for (n=2, nn, newoa = flargest(voa, n) + voa[n-1]; print1(newoa - voa[n-1], ", "); voa = concat(voa, newoa););} \\ Michel Marcus, Mar 24 2015

More terms from Michel Marcus, Mar 24 2015

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

Leroy Quet, Apr 10 2006

Michael De Vlieger, Table of n, a(n) for n = 0..10000

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

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 *)

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

Leroy Quet, Apr 10 2006

Michael De Vlieger, Table of n, a(n) for n = 0..10000

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

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 *)

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

A118028 a(0)=1. 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

1, 3, 5, 9, 13, 19, 25, 32, 40, 50, 60, 71, 83, 97, 111, 126, 142, 159, 177, 197, 217, 238, 260, 283, 307, 333, 359, 386, 414, 443, 473, 504, 537, 570, 604, 639, 675, 712, 750, 789, 830, 871, 913, 956, 1000, 1045, 1091, 1138, 1186, 1235, 1286, 1337, 1389, 1442

Offset: 0

Leroy Quet, Apr 10 2006

Michael De Vlieger, Table of n, a(n) for n = 0..1000

Cf. A118026, A118027, A118029, A118030, A094589.

a = {1}; Do[k = 2; While[Nand[FreeQ[a, k], k >= i], k++]; AppendTo[a, a[[i]] + k], {i, 53}]; a (* Michael De Vlieger, Sep 19 2017 *)

More terms from Joshua Zucker, Jul 27 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

Leroy Quet, Apr 10 2006

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

Michael De Vlieger, Table of n, a(n) for n = 0..1000

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

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 *)

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

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

Leroy Quet, Apr 10 2006

Michael De Vlieger, Table of n, a(n) for n = 1..5000

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

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 *)

More terms from Melissa Donovan (msd181(AT)psu.edu), Apr 23 2006

A094590 a(1) = 1; a(n+1) = a(n) * k(n), where k(n) is the number of elements of {a(j)}, 1<=j<=n, which are <= n.

Original entry on oeis.org

1, 1, 2, 6, 18, 54, 216, 864, 3456, 13824, 55296, 221184, 884736, 3538944, 14155776, 56623104, 226492416, 905969664, 4529848320, 22649241600, 113246208000, 566231040000, 2831155200000, 14155776000000, 70778880000000

Offset: 1

Leroy Quet, Jun 07 2004

Cf. A094589.

More terms from Vladeta Jovovic, Jun 13 2004

cp's OEIS Frontend

A250983 First differences of A094589.

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

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

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A118028 a(0)=1. a(n) = a(n-1) + (smallest integer which is >= n and is missing from the earlier terms of the sequence).

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

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Programs

Mathematica

PARI

Extensions

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

Views

Author

Keywords

Links

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Programs

Mathematica

Extensions

A094590 a(1) = 1; a(n+1) = a(n) * k(n), where k(n) is the number of elements of {a(j)}, 1<=j<=n, which are <= n.

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