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

3, 6, 11, 14, 19, 22, 25, 28, 33, 36, 41, 44, 47, 50, 55, 58, 63, 66, 71, 74, 79, 82, 85, 88, 93, 96, 101, 104, 107, 110, 115, 118, 123, 126, 131, 134, 139, 142, 145, 148, 153, 156, 161, 164, 167, 170, 175, 178, 183, 186, 189, 192, 197

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

Appears to be complement of A026367. - N. J. A. Sloane, Oct 18 2022

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

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

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

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000
• Robbert Fokkink, Gerard Francis Ortega, and Dan Rust, Corner the Empress, arXiv:2204.11805 [math.CO], 2022. See Table 4.
• Wen An Liu and Xiao Zhao, Adjoining to (s,t)-Wythoff's game its P-positions as moves, Discrete Applied Mathematics, Aug 27 2014. See Table 4.
• J. Shallit, Proof of Irvine's conjecture via mechanized guessing, arXiv preprint arXiv:2310.14252 [math.CO], October 22 2023.

Crossrefs

Cf. A026367, A187224, A004526, A285421.

Programs

Mathematica

s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {1, 1, 0}}] &, {0}, 13] (* A285431 *)
Flatten[Position[s, 0]]  (* A026368 *)
Flatten[Position[s, 1]]  (* A026367 *)
(* Clark Kimberling, Apr 28 2017 *)