A128163 -id:A128163 - cp's OEIS frontend

A128162 a(n) = 3^n modulo Fibonacci(n).

0, 0, 1, 0, 3, 1, 3, 9, 31, 34, 37, 81, 137, 347, 487, 690, 355, 1369, 2001, 1926, 5331, 1369, 4823, 8289, 74043, 77951, 188571, 284781, 490766, 166409, 1333373, 1803615, 1516839, 914943, 3619092, 3987873, 17604245, 8506938, 57277423, 24741861

Offset: 1

Alexander Adamchuk, Feb 19 2007

nonn

Numbers k such that a(k) is prime are listed in A128163. Corresponding primes in {a(n)} are {3, 3, 31, 37, 137, 347, 487, 77951, 166409, 13506083561, ...}.

Robert Israel, Table of n, a(n) for n = 1..4783

Cf. A128163, A128161, A057862 (2^n modulo Fibonacci(n)).

f:= n -> 3 &^ n mod combinat:-fibonacci(n):
map(f, [$1..100]); # Robert Israel, Jul 10 2020

Table[PowerMod[3,n,Fibonacci[n]],{n,1,100}]

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

[power_mod(3,n,fibonacci(n))for n in range(1,41)] # - Zerinvary Lajos, Nov 28 2009

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

A128162 a(n) = 3^n modulo Fibonacci(n).

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