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A036136
a(n) = 3^n mod 89.
3
1, 3, 9, 27, 81, 65, 17, 51, 64, 14, 42, 37, 22, 66, 20, 60, 2, 6, 18, 54, 73, 41, 34, 13, 39, 28, 84, 74, 44, 43, 40, 31, 4, 12, 36, 19, 57, 82, 68, 26, 78, 56, 79, 59, 88, 86, 80, 62, 8, 24, 72, 38, 25, 75, 47, 52, 67, 23
OFFSET
0,2
REFERENCES
I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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-44) + a(n-45).
a(n+88) = a(n). (End)
MAPLE
[ seq(primroot(ithprime(i))^j mod ithprime(i), j=0..100) ];
MATHEMATICA
PowerMod[3, Range[0, 100], 89] (* G. C. Greubel, Oct 17 2018 *)
PROG
(PARI) a(n)=lift(Mod(3, 89)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(3, n, 89): n in [0..100]]; // G. C. Greubel, Oct 17 2018
(Python) for n in range(0, 100): print(int(pow(3, n, 89)), end=' ') # Stefano Spezia, Oct 17 2018
(GAP) List([0..60], n->PowerMod(3, n, 89)); # Muniru A Asiru, Oct 17 2018
CROSSREFS
Cf. A000244 (3^n).
Sequence in context: A329023 A001218 A036158 * A271350 A057262 A057232
KEYWORD
nonn,easy
STATUS
approved