A026366 - OEIS

A026366

a(n) = a(m) if a(m) has already occurred exactly once and n = a(m)+2m, else a(n) = least positive integer that has not yet occurred.

1, 2, 1, 3, 4, 2, 5, 6, 7, 8, 3, 9, 10, 4, 11, 12, 13, 14, 5, 15, 16, 6, 17, 18, 7, 19, 20, 8, 21, 22, 23, 24, 9, 25, 26, 10, 27, 28, 29, 30, 11, 31, 32, 12, 33, 34, 13, 35, 36, 14, 37, 38, 39, 40, 15, 41, 42, 16, 43, 44, 45, 46, 17, 47, 48, 18, 49

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..67.

A. S. Fraenkel, Heap games, numeration systems and sequences, arXiv:math/9809074 [math.CO], 1998; Annals of Combinatorics, 2 (1998), 197-210.

J. Shallit, Proof of Irvine's conjecture via mechanized guessing, arXiv preprint arXiv:2310.14252 [math.CO], October 22 2023.

MATHEMATICA

a[n_] := a[n] = Module[{aa, m}, aa = Array[a, n-1]; For[m = 1, m < n, m++, If[n == a[m] + 2m && Count[aa, a[m]] == 1, Return[a[m]]]]; For[m = 1, True, m++, If[FreeQ[aa, m], Return[m]]]]; a[1] = 1; Array[a, 100] (* Jean-François Alcover, Jan 26 2019 *)

CROSSREFS

Cf. A026367, A026368.

Sequence in context: A166711 A026249 A130527 * A209125 A209137 A269752

Adjacent sequences: A026363 A026364 A026365 * A026367 A026368 A026369

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

Description corrected by Aviezri S. Fraenkel

STATUS

approved