A070389 a(n) = 5^n mod 43.
1, 5, 25, 39, 23, 29, 16, 37, 13, 22, 24, 34, 41, 33, 36, 8, 40, 28, 11, 12, 17, 42, 38, 18, 4, 20, 14, 27, 6, 30, 21, 19, 9, 2, 10, 7, 35, 3, 15, 32, 31, 26, 1, 5, 25, 39, 23, 29, 16, 37, 13, 22, 24, 34, 41, 33, 36, 8, 40, 28, 11, 12, 17, 42, 38, 18, 4, 20, 14, 27, 6, 30, 21, 19
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, 0, -1, 1).
Programs
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Magma
[Modexp(5, n, 43): n in [0..80]]; // Bruno Berselli, Mar 22 2016
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Mathematica
PowerMod[5, Range[0, 50], 43] (* G. C. Greubel, Mar 16 2016 *)
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PARI
a(n)=lift(Mod(5,43)^n) \\ Charles R Greathouse IV, Mar 22 2016
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Sage
[power_mod(5,n,43) for n in range(0,74)] # Zerinvary Lajos, Nov 26 2009
Formula
From R. J. Mathar, Apr 20 2010: (Start)
a(n) = a(n-1) - a(n-21) + a(n-22).
G.f.: ( -1-4*x -20*x^2 -14*x^3 +16*x^4 -6*x^5 +13*x^6-21*x^7 +24*x^8 -9*x^9 -2*x^10 -10*x^11 -7*x^12 +8*x^13 -3*x^14 +28*x^15 -32*x^16 +12*x^17 +17*x^18 -x^19 -5*x^20 -26*x^21 ) / ( (x-1)*(1+x)*(x^2-x+1)*(x^6-x^5+x^4-x^3+x^2-x+1)*(x^12+x^11-x^9-x^8+x^6-x^4-x^3+x+1) ). (End)
a(n) = a(n-42). - G. C. Greubel, Mar 16 2016