A128163 Numbers k such that A128162(k) is prime.

5, 7, 9, 11, 13, 14, 15, 26, 30, 53, 66, 82, 155, 189, 225, 261, 625, 870, 1071, 7655, 8191, 8883, 9226, 12246, 70274, 71595, 108009, 127077

Offset: 1

Author

Alexander Adamchuk, Feb 19 2007

Keywords

• hard
• more
• nonn

Comments

Corresponding primes in A128162 are {3, 3, 31, 37, 137, 347, 487, 77951, 166409, 13506083561, ...}.

Crossrefs

Cf. A128162 (3^n modulo Fibonacci(n)), A128161, A057862 (2^n modulo Fibonacci(n)).

Programs

Mathematica

Do[f=PowerMod[3,n,Fibonacci[n]];If[PrimeQ[f],Print[{n,f}]],{n,1,1071}]
Select[Range[72000],PrimeQ[PowerMod[3,#,Fibonacci[#]]]&] (* Harvey P. Dale, Sep 11 2019 *)

PARI

is(n)=ispseudoprime(3^n%fibonacci(n)) \\ Charles R Greathouse IV, Jun 19 2017

PFGW

ABC2 3^$a % F($a)
a: from 5 to 1000000
// Charles R Greathouse IV, Jun 19 2017

Extensions

Corrected and extended by Stefan Steinerberger, Jun 10 2007

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

a(27)-a(28) from Michael S. Branicky, Nov 21 2024