OFFSET
1,1
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
EXAMPLE
For n=1, all numbers p satisfy p=1 (mod n), but p=11 is the least prime that divides F((p-1)/1)=F(p-1)=F(10)=55.
For n=2, all odd numbers, thus all primes p>2, satisfy p=1 (mod n), but p=29 is the first one to divide F((p-1)/2) = F(14) = 377 = 13*29.
For n=5, a(n)=211 is the smallest Artiad, i.e. prime p=1 (mod 5) which divides F((p-1)/5) = F(42) = 211*1269736.
MATHEMATICA
a[1] = 11;
a[n_] := For[p = 1, True, p = p + n, If[PrimeQ[p] && Divisible[Fibonacci[(p - 1)/n], p], Return[p]]];
a /@ Range[100] (* Jean-François Alcover, Oct 14 2019 *)
PROG
(PARI) for(n=1, 99, forprime(p=1, oo, (p-1)%n & next; fibonacci((p-1)/n)%p || print1(p, ", ") || next(2)))
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, Nov 25 2009
STATUS
approved