A128161 Numbers k such that 2^k modulo Fibonacci(k) is prime, i.e., A057862(k) is prime.

5, 7, 9, 13, 14, 19, 25, 88, 100, 113, 130, 440, 503, 2800, 3203, 3346, 4357, 6496, 8822, 16316, 20039, 22381, 30481, 33779, 71864, 110390, 127796, 441190, 457249

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..29.

Maple

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

Mathematica

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

Prog

(PARI) is(n)=ispseudoprime(2^n%fibonacci(n)) \\ Charles R Greathouse IV, Jun 19 2017
(PFGW)
ABC2 2^$a % F($a)
a: from 5 to 1000000
// Charles R Greathouse IV, Jun 19 2017

Crossrefs

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

Sequence in context: A115913 A200268 A251627 * A141106 A047478 A048974

Adjacent sequences: A128158 A128159 A128160 * A128162 A128163 A128164

Keyword

hard,more,nonn

Author

Alexander Adamchuk, Feb 19 2007

Extensions

a(14)-a(19) from Stefan Steinerberger, Jun 10 2007

More terms from Ryan Propper, Jan 11 2008

a(25)-a(26) from Donovan Johnson, Sep 03 2008

a(27) from Charles R Greathouse IV, Jun 20 2017

a(28)-a(29) from Charles R Greathouse IV, Jun 30 2017

Status

approved