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

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• 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.

Crossrefs

Cf. A026367, A026368.

Programs

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 *)

Extensions

Description corrected by Aviezri S. Fraenkel