A036133 a(n) = 5^n mod 73.

1, 5, 25, 52, 41, 59, 3, 15, 2, 10, 50, 31, 9, 45, 6, 30, 4, 20, 27, 62, 18, 17, 12, 60, 8, 40, 54, 51, 36, 34, 24, 47, 16, 7, 35, 29, 72, 68, 48, 21, 32, 14, 70, 58, 71, 63, 23, 42, 64, 28, 67, 43, 69, 53, 46, 11, 55, 56

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,-1,1).

Formula

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

a(n) = a(n-1) - a(n-36) + a(n-37).

a(n+72) = a(n). (End)

Maple

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

Mathematica

PowerMod[5, Range[0, 60], 73] (* Harvey P. Dale, Dec 24 2011 *)

Prog

(PARI) a(n)=lift(Mod(5, 73)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(5, n, 73): n in [0..100]]; // G. C. Greubel, Oct 17 2018
(Python) for n in range(0, 100): print(int(pow(5, n, 73)), end=' ') # Stefano Spezia, Oct 17 2018
(GAP) List([0..60], n->PowerMod(5, n, 73)); # Muniru A Asiru, Oct 17 2018

Crossrefs

Cf. A000351 (5^n).

Sequence in context: A101654 A043106 A147184 * A062671 A225494 A139479

Adjacent sequences: A036130 A036131 A036132 * A036134 A036135 A036136

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved