cp's OEIS Frontend

A026368 a(n) = greatest k such that s(k) = n, where s = A026366.

%I A026368 #30 Aug 03 2025 03:37:23
%S A026368 3,6,11,14,19,22,25,28,33,36,41,44,47,50,55,58,63,66,71,74,79,82,85,
%T A026368 88,93,96,101,104,107,110,115,118,123,126,131,134,139,142,145,148,153,
%U A026368 156,161,164,167,170,175,178,183,186,189,192,197
%N A026368 a(n) = greatest k such that s(k) = n, where s = A026366.
%C A026368 Appears to be complement of A026367. - _N. J. A. Sloane_, Oct 18 2022
%C A026368 Complement of the rank transform of the sequence A004526=(1,1,2,2,3,3,4,4,5,5,...). See A187224.
%C A026368 Positions of 0 in the fixed point of the morphism 0->11, 1->110; see A285431. Conjecture: -2 < n*r - a(n) < 4 for n>=1, where r = 2 + sqrt(3). - _Clark Kimberling_, Apr 29 2017
%C A026368 Also, with an initial 0, appears to be the sequence B' of P-positions in Fraenkel's (2,1)-Wythoff's game. The associated A' sequence is A026367. - _N. J. A. Sloane_, Oct 20 2022
%H A026368 Clark Kimberling, <a href="/A026368/b026368.txt">Table of n, a(n) for n = 1..10000</a>
%H A026368 Robbert Fokkink, Gerard Francis Ortega, and Dan Rust, <a href="https://arxiv.org/abs/2204.11805">Corner the Empress</a>, arXiv:2204.11805 [math.CO], 2022. See Table 4.
%H A026368 Wen An Liu and Xiao Zhao, <a href="http://dx.doi.org/10.1016/j.dam.2014.08.009">Adjoining to (s,t)-Wythoff's game its P-positions as moves</a>, Discrete Applied Mathematics, Aug 27 2014. See Table 4.
%H A026368 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 A026368 s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {1, 1, 0}}] &, {0}, 13] (* A285431 *)
%t A026368 Flatten[Position[s, 0]]  (* A026368 *)
%t A026368 Flatten[Position[s, 1]]  (* A026367 *)
%t A026368 (* _Clark Kimberling_, Apr 28 2017 *)
%Y A026368 Cf. A026367, A187224, A004526, A285421.
%K A026368 nonn
%O A026368 1,1
%A A026368 _Clark Kimberling_