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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 G. C. Greubel, Table of n, a(n) for n = 0..1000 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 Adjacent sequences: A070412 A070413 A070414 * A070416 A070417 A070418 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.)