A338794 - OEIS

%I #37 Nov 19 2020 12:30:28

%S 39,60,69,72,99,102,105,108,111,150,165,180,192,195,198,225,228,231,

%T 240,270,279,282,309,312,315,348,351,381,399,420,441,459,462,465,489,

%U 501,522,588,591,600,615,618,642,645,660,675,702,741,759,771,810,822,825,828

%N Index k of Fibonacci numbers such that F(k)^2 + 1 has no Fibonacci prime factor, where F(k) is the k-th Fibonacci number.

%C Or numbers k such that A338762(k) = 0.

%H Chai Wah Wu, <a href="/A338794/b338794.txt">Table of n, a(n) for n = 1..10000</a>

%e 39 is in the sequence because F(39)^2 + 1 = 63245986^2 + 1 = 73*149*2221*2789*59369 with no Fibonacci prime factors.

%e 38 is not in the sequence because F(38)^2 + 1 = 39088169^2 + 1 =  2*73*149*233*2221*135721. The numbers and 2, 233 are Fibonacci prime factors.

%p a:= proc(n) local F, m, t; F, m, t:=

%p       [1, 2], 0, (<<0|1>, <1|1>>^n)[2, 1]^2+1;

%p       while F[2]<=t do if isprime(F[2]) and irem(t, F[2])=0

%p         then m:=F[2] fi; F:= [F[2], F[1]+F[2]]

%p       od; m

%p     end:

%p for n from 1 to 100 do :

%p if a(n)=0 then printf(`%d, `,n):else fi:

%p od: # program from _Alois P. Heinz_, adapted for the sequence. See A338762.

%o (PARI) isok(n) = {my(i=0, f=0, x=fibonacci(n)^2+1, m=0); while(f < x, i++; f = fibonacci(i); if (ispseudoprime(f) && (x%f) == 0, return (0));); return(1);} \\ _Michel Marcus_, Nov 13 2020

%Y Cf. A000045, A005478, A168063, A245306, A338762.

%K nonn

%O 1,1

%A _Michel Lagneau_, Nov 09 2020