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A036134
a(n) = 3^n mod 79.
3
1, 3, 9, 27, 2, 6, 18, 54, 4, 12, 36, 29, 8, 24, 72, 58, 16, 48, 65, 37, 32, 17, 51, 74, 64, 34, 23, 69, 49, 68, 46, 59, 19, 57, 13, 39, 38, 35, 26, 78, 76, 70, 52, 77, 73, 61, 25, 75, 67, 43, 50, 71, 55, 7, 21, 63, 31, 14
OFFSET
0,2
COMMENTS
Because a(39) = 78, the Legendre symbol (3/79) = -1, meaning that 3 is not a quadratic residue of 79. Furthermore, it means that 3 is prime in Z[sqrt(79)]. - Alonso del Arte, Oct 01 2012
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,-1,1).
FORMULA
From G. C. Greubel, Oct 17 2018: (Start)
a(n) = a(n-1) - a(n-39) + a(n-40).
a(n+78) = a(n). (End)
EXAMPLE
a(4) = 2 because 3^4 = 81 and 81 - 79 = 2.
MAPLE
[ seq(primroot(ithprime(i))^j mod ithprime(i), j=0..100) ];
MATHEMATICA
Table[Mod[3^n, 79], {n, 0, 60}] (* Alonso del Arte, Oct 01 2012 *)
PowerMod[3, Range[0, 100], 79] (* Harvey P. Dale, Feb 21 2024 *)
PROG
(PARI) a(n)=lift(Mod(3, 79)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(3, n, 79): n in [0..100]]; // G. C. Greubel, Oct 17 2018
(Python) for n in range(0, 100): print(int(pow(3, n, 79)), end=' ') # Stefano Spezia, Oct 17 2018
(GAP) List([0..60], n->PowerMod(3, n, 79)); # Muniru A Asiru, Oct 17 2018
CROSSREFS
Cf. A000244 (3^n).
Sequence in context: A126025 A317497 A114181 * A317502 A213912 A070360
KEYWORD
nonn,easy
STATUS
approved