A220979 a(n) = 5^(4n+2) - 5^(3n+2) + 3 * 5^(2n+1) - 5^(n+1) + 1: the left Aurifeuillian factor of 5^(10n+5) - 1.
11, 12851, 9384251, 6054921251, 3808599606251, 2383422998031251, 1490020755615156251, 931310653778075781251, 582075119020843503906251, 363797694444713592519531251, 227373652160169124603222656251, 142108544241637027263641113281251
Offset: 0
Links
- Wikipedia, Cunningham Project
- Index entries for linear recurrences with constant coefficients, signature (781,-101530,2538250,-12203125,9765625).
Programs
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Mathematica
Table[5^(4n+2) - 5^(3n+2) + 3 * 5^(2n+1) - 5^(n+1) + 1, {n, 0, 30}] -
PARI
a(n)=5^(4*n+2)-5^(3*n+2)+3*5^(2*n+1)-5^(n+1)+1 \\ Charles R Greathouse IV, Sep 28 2015
Formula
Aurifeuillian factorization: 5^(10n+5) - 1 = (5^(2n+1) - 1) * a(n) * A220980(n).
G.f.: -(4296875*x^4+2662500*x^3+464450*x^2+4260*x+11) / ((x-1)*(5*x-1)*(25*x-1)*(125*x-1)*(625*x-1)). - Colin Barker, Jan 03 2013
Comments