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

0,2

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).

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)

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 *)

Prog

(PARI) a(n)=lift(Mod(2, 101)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(2, n, 101): n in [0..100]]; // G. C. Greubel, Oct 18 2018
(GAP) a:=List([0..60], n->PowerMod(2, n, 101));; Print(a); # Muniru A Asiru, Jan 26 2019

Crossrefs

Cf. A000079 (2^n).

Sequence in context: A343926 A223700 A036140 * A000855 A036135 A036131

Adjacent sequences: A036135 A036136 A036137 * A036139 A036140 A036141

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved