A026368 - OEIS

%I #26 Oct 24 2023 11:46:42

%S 3,6,11,14,19,22,25,28,33,36,41,44,47,50,55,58,63,66,71,74,79,82,85,

%T 88,93,96,101,104,107,110,115,118,123,126,131,134,139,142,145,148,153,

%U 156,161,164,167,170,175,178,183,186,189,192,197

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

%C Appears to be complement of A026367. - _N. J. A. Sloane_, Oct 18 2022

%C Complement of the rank transform of the sequence A004526=(1,1,2,2,3,3,4,4,5,5,...).  See A187224.

%C 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 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 20221

%H Clark Kimberling, <a href="/A026368/b026368.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 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 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 s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {1, 1, 0}}] &, {0}, 13] (* A285431 *)

%t Flatten[Position[s, 0]]  (* A026368 *)

%t Flatten[Position[s, 1]]  (* A026367 *)

%t (* _Clark Kimberling_, Apr 28 2017 *)

%Y Cf. A026367, A187224, A004526, A285421.

%K nonn

%O 1,1

%A _Clark Kimberling_