A036140 a(n) = 2^n mod 107.

1, 2, 4, 8, 16, 32, 64, 21, 42, 84, 61, 15, 30, 60, 13, 26, 52, 104, 101, 95, 83, 59, 11, 22, 44, 88, 69, 31, 62, 17, 34, 68, 29, 58, 9, 18, 36, 72, 37, 74, 41, 82, 57, 7, 14, 28, 56, 5, 10, 20, 40, 80, 53, 106, 105, 103

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Cyclical with a cycle length of 106. - Harvey P. Dale, May 07 2013

References

• I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1).

Crossrefs

Cf. A000079 (2^n).

Programs

GAP

List([0..55],n->PowerMod(2,n,107)); # Muniru A Asiru, Oct 18 2018

Magma

[Modexp(2, n, 107): n in [0..100]]; // G. C. Greubel, Oct 18 2018

Maple

[ seq(primroot(ithprime(i))^j mod ithprime(i),j=0..100) ];

Mathematica

PowerMod[2,Range[0,60],107] (* Harvey P. Dale, May 07 2013 *)

PARI

a(n)=lift(Mod(2,107)^n) \\ Charles R Greathouse IV, Mar 22 2016

Formula

From G. C. Greubel, Oct 18 2018: (Start)

a(n+106) = a(n).

a(n) = a(n-1) - a(n-53) + a(n-54). (End)