The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
B. Avila and T. Khovanova, Free Fibonacci Sequences, arXiv preprint arXiv:1403.4614 [math.NT], 2014 and J. Int. Seq. 17 (2014) # 14.8.5.
FORMULA
{p in A000040: A001177(p) < 1+p}.
MAPLE
filter:= proc(n) local i, a, b, c;
if not isprime(n) then return false fi;
a:= 0; b:= 1;
for i from 1 to n-1 do
c:= b;
b:= a+b mod n; if b = 0 then return true fi;
a:= c;
od;
false
end proc:
select(filter, [seq(i, i=3..1000, 2)]); # Robert Israel, Sep 01 2020
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-François Alcover, Oct 21 2013 *)
PROG
(Sage)
def isA230359(p):
return any(p.divides(fibonacci(k)) for k in (1..p))
print([p for p in primes(1, 500) if isA230359(p)]) # Peter Luschny, Nov 01 2019
CROSSREFS
A002144 is a subsequence.
Sequence in context: A087759 A234644 A299791 * A161548 A090320 A085909
KEYWORD
nonn
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 17 15:57 EDT 2024. Contains 373463 sequences. (Running on oeis4.)