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A230359 Prime numbers p such that their Fibonacci entry points are less than p+1. 4
5, 11, 13, 17, 19, 29, 31, 37, 41, 47, 53, 59, 61, 71, 73, 79, 89, 97, 101, 107, 109, 113, 131, 137, 139, 149, 151, 157, 173, 179, 181, 191, 193, 197, 199, 211, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 373, 379, 389, 397, 401, 409, 419, 421, 431, 433, 439, 449, 457, 461, 479, 491, 499 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For these primes p there exists a Fibonacci like sequence that doesn't contain multiples of p.

For other primes p the Fibonacci entry points are p+1. These primes are sequence A000057: Primes dividing all Fibonacci sequences.

LINKS

Table of n, a(n) for n=1..75.

B. Avila and T. Khovanova, Free Fibonacci Sequences, arXiv preprint arXiv:1403.4614, 2014 and J. Int. Seq. 17 (2014) # 14.8.5

FORMULA

{p in A000040: A001177(p) < 1+p}.

MATHEMATICA

A001177[n_] := For[k = 1, True, k++, If[Divisible[Fibonacci[k], n], Return[k]]]; A230359 = Reap[For[p = 2, p <= 499, p = NextPrime[p], If[A001177[p] < 1+p, Sow[p]]]][[2, 1]] (* Jean-Fran├žois Alcover, Oct 21 2013 *)

CROSSREFS

Cf. A001177, A001602.

Sequence in context: A087759 A234644 A299791 * A161548 A090320 A085909

Adjacent sequences:  A230356 A230357 A230358 * A230360 A230361 A230362

KEYWORD

nonn

AUTHOR

Brandon Avila and Tanya Khovanova, Oct 16 2013

STATUS

approved

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Last modified May 24 10:48 EDT 2019. Contains 323529 sequences. (Running on oeis4.)