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A036141
a(n) = 6^n mod 109.
1
1, 6, 36, 107, 97, 37, 4, 24, 35, 101, 61, 39, 16, 96, 31, 77, 26, 47, 64, 57, 15, 90, 104, 79, 38, 10, 60, 33, 89, 98, 43, 40, 22, 23, 29, 65, 63, 51, 88, 92, 7, 42, 34, 95, 25, 41, 28, 59, 27, 53, 100, 55, 3, 18, 108
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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1).
FORMULA
From G. C. Greubel, Oct 18 2018: (Start)
a(n + 108) = a(n).
a(n) = a(n-1) - a(n-54) + a(n-55). (End)
MAPLE
[ seq(primroot(ithprime(i))^j mod ithprime(i), j=0..100) ];
MATHEMATICA
PowerMod[6, Range[0, 60], 109] (* Harvey P. Dale, Apr 27 2018 *)
PROG
(PARI) a(n)=lift(Mod(6, 109)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(6, n, 109): n in [0..100]]; // G. C. Greubel, Oct 18 2018
(GAP) List([0..55], n->PowerMod(6, n, 109)); # Muniru A Asiru, Oct 18 2018
CROSSREFS
Cf. A000400 (6^n).
Sequence in context: A207495 A207249 A060521 * A270205 A207443 A207437
KEYWORD
nonn,easy
STATUS
approved