A057862 a(n) = 2^n mod Fibonacci(n).

0, 0, 0, 1, 2, 0, 11, 4, 2, 34, 1, 64, 37, 173, 438, 394, 118, 1160, 1663, 1, 6466, 14508, 20764, 38368, 18257, 99928, 64234, 202972, 15836, 410224, 184593, 1520257, 538006, 2773540, 5886173, 9996832, 5132559, 9902536, 21703576, 33466456

Offset: 1

Author

Henry Bottomley, Sep 08 2000

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..4782

Crossrefs

Cf. A000045, A000079.

Programs

GAP

List([1..42],n->PowerMod(2,n,Fibonacci(n))); # Muniru A Asiru, Jul 13 2018

Maple

seq(2 &^n mod combinat:-fibonacci(n), n=1..100); # Robert Israel, Jul 13 2018

Mathematica

Table[Mod[2^n,Fibonacci[n]],{n,1,80}] (* Vladimir Joseph Stephan Orlovsky, Apr 03 2011*)
Table[PowerMod[2,n,Fibonacci[n]],{n,40}] (* Harvey P. Dale, Dec 30 2018 *)

PARI

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

Sage

[power_mod(2,n,fibonacci(n))for n in range(1,41)] # Zerinvary Lajos, Nov 28 2009

Formula

a(n) = A000079(n) - A057861(n)*A000045(n)