A036138 a(n) = 2^n mod 101.

1, 2, 4, 8, 16, 32, 64, 27, 54, 7, 14, 28, 56, 11, 22, 44, 88, 75, 49, 98, 95, 89, 77, 53, 5, 10, 20, 40, 80, 59, 17, 34, 68, 35, 70, 39, 78, 55, 9, 18, 36, 72, 43, 86, 71, 41, 82, 63, 25, 50, 100, 99, 97, 93, 85, 69, 37

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• 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,-1,1).

Crossrefs

Cf. A000079 (2^n).

Programs

GAP

a:=List([0..60],n->PowerMod(2,n,101));; Print(a); # Muniru A Asiru, Jan 26 2019

Magma

[Modexp(2, n, 101): 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],101] (* Harvey P. Dale, Mar 19 2013 *)

PARI

a(n)=lift(Mod(2,101)^n) \\ Charles R Greathouse IV, Mar 22 2016

Formula

From G. C. Greubel, Oct 17 2018: (Start)

a(n) = a(n-1) - a(n-50) + a(n-51).

a(n+100) = a(n). (End)