A036128 a(n) = 2^n mod 53.

1, 2, 4, 8, 16, 32, 11, 22, 44, 35, 17, 34, 15, 30, 7, 14, 28, 3, 6, 12, 24, 48, 43, 33, 13, 26, 52, 51, 49, 45, 37, 21, 42, 31, 9, 18, 36, 19, 38, 23, 46, 39, 25, 50, 47, 41, 29, 5, 10, 20, 40, 27, 1, 2, 4, 8, 16, 32, 11, 22

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,-1,1).

Formula

a(n) = a(n-1) - a(n-26) + a(n-27). - R. J. Mathar, Feb 06 2011

a(n) = a(n+52). - R. J. Mathar, Jun 04 2016

Maple

i := pi(53) ; [ seq(primroot(ithprime(i))^j mod ithprime(i), j=0..100) ];

Mathematica

PowerMod[2, Range[0, 60], 53] (* Harvey P. Dale, Apr 11 2013 *)

Prog

(PARI) a(n)=lift(Mod(2, 53)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(2, n, 53): n in [0..100]]; // G. C. Greubel, Oct 17 2018
(Python) for n in range(0, 100): print(int(pow(2, n, 53)), end=' ') # Stefano Spezia, Oct 17 2018
(GAP) List([0..60], n->PowerMod(2, n, 53)); # Muniru A Asiru, Oct 17 2018

Crossrefs

Cf. A000079 (2^n).

Sequence in context: A364628 A328753 A119990 * A073477 A220105 A070351

Adjacent sequences: A036125 A036126 A036127 * A036129 A036130 A036131

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved