OFFSET
0,3
COMMENTS
Numbers k such that k divides Fibonacci(k) are listed in A023172.
All powers of 5 belong to A023172.
5^n divides Fibonacci(5^n).
a(n) == 1 (mod 1000).
{a(n+1)/a(n)} = {1, 3001, 158414167964045700001, 62351961552434956321060201440347372028390478647963811251289490034177804212636326088548682319305439375001, ...}.
FORMULA
a(n) = Fibonacci(5^n) / 5^n.
a(n+1) = 5^(4*n+1)*a(n)^5 - 5^(2*n+1)*a(n)^3 + a(n) with a(0) = 1. - Peter Bala, Nov 24 2022
MAPLE
a := proc(n) option remember; if n = 0 then 1 else 5^(4*n-3)*a(n-1)^5 - 5^(2*n-1)*a(n-1)^3 + a(n-1) end if; end proc: seq(a(n), n = 0..5); # Peter Bala, Nov 24 2022
MATHEMATICA
Table[ Fibonacci[ 5^n ] / 5^n, {n, 0, 4} ]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alexander Adamchuk, May 11 2007
STATUS
approved