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

1,2

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

Table of n, a(n) for n=1..64.

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.

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 *)

Crossrefs

Cf. A000045, A004201.

Sequence in context: A187345 A179185 A270198 * A344154 A065871 A128291

Adjacent sequences: A133509 A133510 A133511 * A133513 A133514 A133515

Keyword

easy,nonn

Author

Jonathan Vos Post, Nov 30 2007

Extensions

Data corrected by Giovanni Resta, Jun 20 2016

Status

approved