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

Author

Alexander Adamchuk, Feb 19 2007

Keywords

• nonn

Comments

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, ...}.

Links

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

Crossrefs

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

Programs

Maple

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

Mathematica

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

PARI

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

Sage

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