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A338794 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. 5
39, 60, 69, 72, 99, 102, 105, 108, 111, 150, 165, 180, 192, 195, 198, 225, 228, 231, 240, 270, 279, 282, 309, 312, 315, 348, 351, 381, 399, 420, 441, 459, 462, 465, 489, 501, 522, 588, 591, 600, 615, 618, 642, 645, 660, 675, 702, 741, 759, 771, 810, 822, 825, 828 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000

EXAMPLE

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

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.

MAPLE

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

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

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

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

      od; m

    end:

for n from 1 to 100 do :

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

od: # program from Alois P. Heinz, adapted for the sequence. See A338762.

PROG

(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

CROSSREFS

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

Sequence in context: A168530 A253436 A253429 * A050780 A039353 A043176

Adjacent sequences:  A338791 A338792 A338793 * A338795 A338796 A338797

KEYWORD

nonn

AUTHOR

Michel Lagneau, Nov 09 2020

STATUS

approved

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Last modified September 16 18:26 EDT 2021. Contains 347473 sequences. (Running on oeis4.)