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Primes p such that F(p-(p/5)) is the first Fibonacci number that p divides.
5

%I #14 Jun 22 2024 06:22:52

%S 2,3,5,7,11,19,23,31,43,59,67,71,79,83,103,127,131,163,167,179,191,

%T 223,227,239,251,271,283,311,359,367,379,383,419,431,439,443,463,467,

%U 479,487,491,499,503,523,547,571,587,599,607,631,643,647,659,683,719,727,739,751,787,823,827

%N Primes p such that F(p-(p/5)) is the first Fibonacci number that p divides.

%C The n-th prime p is in this sequence iff A001602(n) = p-(5/p) (that is the maximum possible value of A001602(n)).

%H Amiram Eldar, <a href="/A079346/b079346.txt">Table of n, a(n) for n = 1..10000</a>

%e 7 belongs to this sequence since (7/5) = -1, F(8) = 21 and 7 does not divide F(1) to F(7).

%o (PARI) forprime (p=2,500, wss=p-kronecker(5,p); for(n=1, wss, if( fibonacci(n)%p==0, if( n==wss, print1(p","), break) ) ))

%Y Union of A000057, A106535 and {5}.

%Y Cf. A001602, A079347, A079348, A079349.

%K nonn

%O 1,1

%A _Jon Perry_, Jan 04 2003

%E Corrected and edited by _Max Alekseyev_, Nov 23 2007