A070424 a(n) = 7^n mod 41.
1, 7, 8, 15, 23, 38, 20, 17, 37, 13, 9, 22, 31, 12, 2, 14, 16, 30, 5, 35, 40, 34, 33, 26, 18, 3, 21, 24, 4, 28, 32, 19, 10, 29, 39, 27, 25, 11, 36, 6, 1, 7, 8, 15, 23, 38, 20, 17, 37, 13, 9, 22, 31, 12, 2, 14, 16, 30, 5, 35, 40, 34, 33, 26, 18, 3, 21, 24, 4, 28, 32, 19, 10, 29, 39
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- 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, -1, 1).
Programs
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Magma
[Modexp(7, n, 41): n in [0..100]]; // Bruno Berselli, Mar 22 2016
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Mathematica
PowerMod[7, Range[0, 74], 41] (* Alonso del Arte, Oct 12 2012 *)
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PARI
a(n)=lift(Mod(7,41)^n) \\ Charles R Greathouse IV, Mar 22 2016
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Sage
[power_mod(7,n,41)for n in range(0,75)] # Zerinvary Lajos, Nov 27 2009
Formula
From R. J. Mathar, Apr 20 2010: (Start)
a(n) = a(n - 1) - a(n - 20) + a(n - 21).
G.f.: ( -1 -6*x -x^2 -7*x^3 -8*x^4 -15*x^5 +18*x^6 +3*x^7 -20*x^8 + 24*x^9 +4*x^10 -13*x^11 -9*x^12 +19*x^13 +10*x^14 -12*x^15 -2*x^16 - 14*x^17 +25*x^18 -30*x^19 -6*x^20 ) / ( (x - 1)*(x^4 + 1)*(x^16 -x^12 + x^8 -x^4 +1) ). (End)
a(n) = a(n-40). - G. C. Greubel, Mar 22 2016
Comments