A133512 Accept F(1), reject F(1), accept F(2), reject F(2), accept F(3), ...,.

1, 3, 5, 6, 9, 10, 11, 15, 16, 17, 18, 19, 25, 26, 27, 28, 29, 30, 31, 32, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118

Offset: 1

Author

Jonathan Vos Post, Nov 30 2007

Keywords

• easy
• nonn

Comments

Start with natural numbers, then A004201 Accept one, reject one, accept two, reject two, ..., but this new analogous sequence functionally composes this with A000045 Fibonacci numbers.

a(n+1) is also the length of the shortest prefix of the Fibonacci word (A003849) containing some length-n block twice. - Jeffrey Shallit, May 15 2018

Complement of A344953; i.e., positions of words in A344953 that end with 0. - Clark Kimberling, Jun 12 2021

Links

• Yann Bugeaud and Dong Han Kim, On the b-ary expansions of log(1+1/a) and e, Arxiv preprint arXiv:1510.00282 [math.NT], October 1 2015.
• Yann Bugeaud and Dong Han Kim, On the b-ary expansions of log(1+1/a) and e, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 17 (2017), 931-947.

Crossrefs

Cf. A000045, A004201.

Programs

Mathematica

L = {}; x = 1; Do[L = Join[L, Range[x, x + Fibonacci[n] - 1]]; x += 2 * Fibonacci[n], {n, 9}]; L (* Giovanni Resta, Jun 20 2016 *)

Extensions

Data corrected by Giovanni Resta, Jun 20 2016