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

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

Author

Leroy Quet, Apr 10 2006

Keywords

• easy
• nonn

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

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

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