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A036140
a(n) = 2^n mod 107.
3
1, 2, 4, 8, 16, 32, 64, 21, 42, 84, 61, 15, 30, 60, 13, 26, 52, 104, 101, 95, 83, 59, 11, 22, 44, 88, 69, 31, 62, 17, 34, 68, 29, 58, 9, 18, 36, 72, 37, 74, 41, 82, 57, 7, 14, 28, 56, 5, 10, 20, 40, 80, 53, 106, 105, 103
OFFSET
0,2
COMMENTS
Cyclical with a cycle length of 106. - Harvey P. Dale, May 07 2013
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, -1, 1).
FORMULA
From G. C. Greubel, Oct 18 2018: (Start)
a(n+106) = a(n).
a(n) = a(n-1) - a(n-53) + a(n-54). (End)
MAPLE
[ seq(primroot(ithprime(i))^j mod ithprime(i), j=0..100) ];
MATHEMATICA
PowerMod[2, Range[0, 60], 107] (* Harvey P. Dale, May 07 2013 *)
PROG
(PARI) a(n)=lift(Mod(2, 107)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(2, n, 107): n in [0..100]]; // G. C. Greubel, Oct 18 2018
(GAP) List([0..55], n->PowerMod(2, n, 107)); # Muniru A Asiru, Oct 18 2018
CROSSREFS
Cf. A000079 (2^n).
Sequence in context: A201920 A343926 A223700 * A036138 A000855 A036135
KEYWORD
nonn,easy
STATUS
approved