So why accept? (was: Primefree sequences in the OEIS.)

[David Wilson]

> Why would every
> 15th Fibonacci number be divisible by 10? It's true, at least for the
> first thousand Fibonacci numbers.
>
> Alonso

This follows from two well-known facts about the Fibonaccis.

1.  Every n >= 1 divides some Fib(k)
2.  For every k >= 1, n >= 1, Fib(k) | Fib(kn).

Given these, we can show that for some f(n),

Fib(k) == 0 (mod n)  <=>   k == 0 (mod f(n)).

f(n) is given by A001177(n).  A001177(10) = 15, so every 15th
Fibonacci is divisible by 10.