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A036138
a(n) = 2^n mod 101.
3
1, 2, 4, 8, 16, 32, 64, 27, 54, 7, 14, 28, 56, 11, 22, 44, 88, 75, 49, 98, 95, 89, 77, 53, 5, 10, 20, 40, 80, 59, 17, 34, 68, 35, 70, 39, 78, 55, 9, 18, 36, 72, 43, 86, 71, 41, 82, 63, 25, 50, 100, 99, 97, 93, 85, 69, 37
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,-1,1).
FORMULA
From G. C. Greubel, Oct 17 2018: (Start)
a(n) = a(n-1) - a(n-50) + a(n-51).
a(n+100) = a(n). (End)
MAPLE
[ seq(primroot(ithprime(i))^j mod ithprime(i), j=0..100) ];
MATHEMATICA
PowerMod[2, Range[0, 60], 101] (* Harvey P. Dale, Mar 19 2013 *)
PROG
(PARI) a(n)=lift(Mod(2, 101)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(2, n, 101): n in [0..100]]; // G. C. Greubel, Oct 18 2018
(GAP) a:=List([0..60], n->PowerMod(2, n, 101));; Print(a); # Muniru A Asiru, Jan 26 2019
CROSSREFS
Cf. A000079 (2^n).
Sequence in context: A343926 A223700 A036140 * A000855 A036135 A036131
KEYWORD
nonn,easy
STATUS
approved