A118029 - OEIS

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

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OFFSET

0,2

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

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 *)

PROG

(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

CROSSREFS

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

Sequence in context: A243112 A230127 A059793 * A049322 A014557 A023598

Adjacent sequences: A118026 A118027 A118028 * A118030 A118031 A118032

KEYWORD

easy,nonn

AUTHOR

Leroy Quet, Apr 10 2006

EXTENSIONS

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

More terms from Joshua Zucker, Jul 27 2006

STATUS

approved