%I #26 Jun 13 2021 03:22:36

%S 5,7,9,13,14,19,25,88,100,113,130,440,503,2800,3203,3346,4357,6496,

%T 8822,16316,20039,22381,30481,33779,71864,110390,127796,441190,457249

%N Numbers k such that 2^k modulo Fibonacci(k) is prime, i.e., A057862(k) is prime.

%C Corresponding primes in A057862 are {2, 11, 2, 37, 173, 1663, 18257, 447876604131364627, 55437674149894825801, ...}.

%p select(n->isprime(2 &^n mod combinat:-fibonacci(n)),[$1..3000]); # _Muniru A Asiru_, Jul 17 2018

%t Do[f=PowerMod[2,n,Fibonacci[n]];If[PrimeQ[f],Print[{n,f}]],{n,1,503}]

%o (PARI) is(n)=ispseudoprime(2^n%fibonacci(n)) \\ _Charles R Greathouse IV_, Jun 19 2017

%o (PFGW)

%o ABC2 2^$a % F($a)

%o a: from 5 to 1000000

%o // _Charles R Greathouse IV_, Jun 19 2017

%Y Cf. A057862 = 2^n modulo Fibonacci(n). Cf. A128162, A128163.

%K hard,more,nonn

%O 1,1

%A _Alexander Adamchuk_, Feb 19 2007

%E a(14)-a(19) from _Stefan Steinerberger_, Jun 10 2007

%E More terms from _Ryan Propper_, Jan 11 2008

%E a(25)-a(26) from _Donovan Johnson_, Sep 03 2008

%E a(27) from _Charles R Greathouse IV_, Jun 20 2017

%E a(28)-a(29) from _Charles R Greathouse IV_, Jun 30 2017