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A036123
a(n) = 3^n mod 31.
3
1, 3, 9, 27, 19, 26, 16, 17, 20, 29, 25, 13, 8, 24, 10, 30, 28, 22, 4, 12, 5, 15, 14, 11, 2, 6, 18, 23, 7, 21, 1, 3, 9, 27, 19, 26, 16, 17, 20, 29, 25, 13, 8, 24, 10, 30, 28, 22, 4, 12, 5, 15, 14, 11, 2, 6, 18, 23, 7, 21, 1, 3
OFFSET
0,2
REFERENCES
I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1).
FORMULA
a(n) = a(n+30). - R. J. Mathar, Jun 04 2016
a(n) = a(n-1) - a(n-15) + a(n-16). - G. C. Greubel, Oct 16 2018
a(n) = 31 - a(n+15) for all n in Z. - Michael Somos, Oct 17 2018
MAPLE
[ seq(primroot(ithprime(i))^j mod ithprime(i), j=0..100) ];
MATHEMATICA
PowerMod[3, Range[0, 100], 31] (* G. C. Greubel, Oct 16 2018 *)
PROG
(PARI) a(n)=lift(Mod(3, 31)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(3, n, 31): n in [0..100]]; // G. C. Greubel, Oct 18 2018
(GAP) List([0..65], n->PowerMod(3, n, 31)); # Muniru A Asiru, Oct 18 2018
CROSSREFS
Cf. A000244 (3^n).
Sequence in context: A070358 A321542 A321540 * A168427 A070344 A070357
KEYWORD
nonn,easy
STATUS
approved