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A070415
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a(n) = 7^n mod 31.
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2
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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
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
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FORMULA
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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)
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MATHEMATICA
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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