A220980 a(n) = 5^(4n+2) + 5^(3n+2) + 3 * 5^(2n+1) + 5^(n+1) + 1: the right Aurifeuillian factor of 5^(10n+5) - 1.

71, 19151, 10165751, 6152578751, 3820806643751, 2384948876968751, 1490211490478593751, 931334495635986718751, 582078099253082277343751, 363798066973743438730468751, 227373698726297855377246093751, 142108550062403118610382324218751

Offset: 0

Author

Stuart Clary, Dec 27 2012

Keywords

• nonn
• easy

Comments

The corresponding left Aurifeuillian factor is A220979.

Links

• Wikipedia, Cunningham Project
• Index entries for linear recurrences with constant coefficients, signature (781,-101530,2538250,-12203125,9765625).

Crossrefs

Cf. A092440, A085601, A220978, A198410, A220979-A220990.

Programs

Mathematica

Table[5^(4n+2) + 5^(3n+2) + 3 * 5^(2n+1) + 5^(n+1) + 1, {n, 0, 20}]

Formula

Aurifeuillian factorization: 5^(10n+5) - 1 = (5^(2n+1) - 1) * A220979(n) * a(n).

G.f.: -(27734375*x^4-22687500*x^3+2417450*x^2-36300*x+71) / ((x-1)*(5*x-1)*(25*x-1)*(125*x-1)*(625*x-1)). [Colin Barker, Jan 03 2013]