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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.

%I A026366 #24 Oct 24 2023 11:46:50
%S A026366 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,
%T A026366 21,22,23,24,9,25,26,10,27,28,29,30,11,31,32,12,33,34,13,35,36,14,37,
%U A026366 38,39,40,15,41,42,16,43,44,45,46,17,47,48,18,49
%N 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.
%H A026366 A. S. Fraenkel, <a href="https://arxiv.org/abs/math/9809074">Heap games, numeration systems and sequences</a>, arXiv:math/9809074 [math.CO], 1998; Annals of Combinatorics, 2 (1998), 197-210.
%H A026366 J. Shallit, <a href="https://arxiv.org/abs/2310.14252">Proof of Irvine's conjecture via mechanized guessing</a>, arXiv preprint arXiv:2310.14252 [math.CO], October 22 2023.
%t A026366 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 *)
%Y A026366 Cf. A026367, A026368.
%K A026366 nonn
%O A026366 1,2
%A A026366 _Clark Kimberling_
%E A026366 Description corrected by _Aviezri S. Fraenkel_