A128935 a(n) = Fibonacci(5^n) / 5^n.

1, 1, 3001, 475400918060101145703001, 29642179764875707696452732234250095350341524541114277856812964100763567848899514572925690068090872073476146381237687662210078001

Offset: 0

Author

Alexander Adamchuk, May 11 2007

Keywords

• nonn
• easy

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, ...}.

Crossrefs

Cf. A023172, A121169, A121170, A058635, A045529.

Programs

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} ]

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