A070340 a(n) = 2^n mod 39.
1, 2, 4, 8, 16, 32, 25, 11, 22, 5, 10, 20, 1, 2, 4, 8, 16, 32, 25, 11, 22, 5, 10, 20, 1, 2, 4, 8, 16, 32, 25, 11, 22, 5, 10, 20, 1, 2, 4, 8, 16, 32, 25, 11, 22, 5, 10, 20, 1, 2, 4, 8, 16, 32, 25, 11, 22, 5, 10, 20, 1, 2, 4, 8, 16, 32, 25, 11, 22, 5, 10, 20
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,-1,1,0,0,-1,1)
Programs
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GAP
List([0..83],n->PowerMod(2,n,39)); # Muniru A Asiru, Jan 30 2019
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Mathematica
PowerMod[2, Range[0, 50], 39] (* G. C. Greubel, Mar 12 2016 *)
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PARI
a(n)=lift(Mod(2,39)^n) \\ Charles R Greathouse IV, Mar 22 2016
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Sage
[power_mod(2,n,39)for n in range(0,72)] # Zerinvary Lajos, Nov 03 2009
Formula
From R. J. Mathar, Feb 06 2011: (Start)
a(n) = a(n-1) - a(n-4) + a(n-5) - a(n-8) + a(n-9).
G.f.: ( -1-x-2*x^2-4*x^3-9*x^4-17*x^5+5*x^6+10*x^7-20*x^8 ) / ( (x-1)*(1+x+x^2)*(x^2-x+1)*(x^4-x^2+1) ). (End)
a(n) = a(n-12). - G. C. Greubel, Mar 12 2016