A128162 -id:A128162 - cp's OEIS frontend

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

Alexander Adamchuk, Feb 19 2007

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

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

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 *)

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

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

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

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

Original entry on oeis.org

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

Alexander Adamchuk, Feb 19 2007

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

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

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

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

is(n)=ispseudoprime(2^n%fibonacci(n)) \\ Charles R Greathouse IV, Jun 19 2017

ABC2 2^$a % F($a)
a: from 5 to 1000000
// Charles R Greathouse IV, Jun 19 2017

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

cp's OEIS Frontend

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

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