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A070415 a(n) = 7^n mod 31. 2
1, 7, 18, 2, 14, 5, 4, 28, 10, 8, 25, 20, 16, 19, 9, 1, 7, 18, 2, 14, 5, 4, 28, 10, 8, 25, 20, 16, 19, 9, 1, 7, 18, 2, 14, 5, 4, 28, 10, 8, 25, 20, 16, 19, 9, 1, 7, 18, 2, 14, 5, 4, 28, 10, 8, 25, 20, 16, 19, 9, 1, 7, 18, 2, 14, 5, 4, 28, 10, 8, 25, 20, 16, 19, 9, 1, 7, 18, 2, 14, 5, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Sequence is periodic with period length of 15. That a(15) = 1 means that 31 is not prime in Z[sqrt(7)], being factorable as (-1)*(9 - 4*sqrt(7))(9 + 4*sqrt(7)). - Alonso del Arte, Oct 11 2012
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
FORMULA
From R. J. Mathar, Apr 20 2010: (Start)
a(n) = a(n - 15).
G.f.: ( -1 -7*x -18*x^2 -2*x^3 -14*x^4 -5*x^5 -4*x^6 -28*x^7 -10*x^8 -8*x^9 -25*x^10 -20*x^11 -16*x^12 -19*x^13 -9*x^14 ) / ( (x-1)*(1 +x^4 + x^3 +x^2 +x)*(1 +x +x^2)*(1 -x +x^3 -x^4 +x^5 -x^7 +x^8) ). (End)
MATHEMATICA
PowerMod[7, Range[0, 90], 31] (* Harvey P. Dale, Jul 23 2011 *)
PROG
(Sage) [power_mod(7, n, 31) for n in range(0, 82)] # Zerinvary Lajos, Nov 27 2009
(PARI) a(n) = lift(Mod(7, 31)^n); \\ Altug Alkan, Mar 20 2016
(Magma) [Modexp(7, n, 31): n in [0..100]]; // Bruno Berselli, Mar 22 2016
CROSSREFS
Sequence in context: A138491 A022511 A113613 * A034083 A185455 A103570
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 12 2002
STATUS
approved

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Last modified February 23 00:50 EST 2024. Contains 370265 sequences. (Running on oeis4.)