A128161 -id:A128161 - 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

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

Original entry on oeis.org

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

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Sage