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A036135
a(n) = 2^n mod 83.
3
1, 2, 4, 8, 16, 32, 64, 45, 7, 14, 28, 56, 29, 58, 33, 66, 49, 15, 30, 60, 37, 74, 65, 47, 11, 22, 44, 5, 10, 20, 40, 80, 77, 71, 59, 35, 70, 57, 31, 62, 41, 82, 81, 79, 75, 67, 51, 19, 38, 76, 69, 55, 27, 54, 25, 50, 17
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,-1,1).
FORMULA
From G. C. Greubel, Oct 17 2018: (Start)
a(n) = a(n-1) - a(n-41) + a(n-42).
a(n+82) = a(n). (End)
MAPLE
[ seq(primroot(ithprime(i))^j mod ithprime(i), j=0..100) ];
MATHEMATICA
PowerMod[2, Range[0, 100], 83] (* G. C. Greubel, Oct 17 2018 *)
PROG
(PARI) a(n)=lift(Mod(2, 83)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Python) for n in range(0, 100): print(int(pow(2, n, 83)), end=' ') # Stefano Spezia, Oct 17 2018
(GAP) List([0..60], n->PowerMod(2, n, 83)); # Muniru A Asiru, Oct 17 2018
(Magma) [Modexp(2, n, 83): n in [0..100]]; // G. C. Greubel, Oct 18 2018
CROSSREFS
CF. A000079 (2^n).
Sequence in context: A036140 A036138 A000855 * A036131 A115424 A372944
KEYWORD
nonn,easy
STATUS
approved