A220983 The left Aurifeuillian factor of 7^(14n+7) + 1.

113, 34925927, 4651514210561, 556919483179733591, 65684998500756890925713, 7730533744900130305342957127, 909535949164303794596648514307361, 107006774488854204226839526889653524791, 12589253114717671385404089651370543317211313

Offset: 0

Author

Stuart Clary, Dec 27 2012

Keywords

• nonn
• easy

Comments

The corresponding right Aurifeuillian factor is A220984.

Links

• Wikipedia, Cunningham Project
• Index entries for linear recurrences with constant coefficients, signature (137257, -2354918349, 5670354183893, -1944931485075299, 95029449572634843, -651636050170246351, 558545864083284007).

Crossrefs

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

Programs

Mathematica

Table[7^(6n+3) - 7^(5n+3) + 3 * 7^(4n+2) - 7^(3n+2) + 3 * 7^(2n+1) - 7^(n+1) + 1, {n, 0, 20}]

Formula

a(n) = 7^(6n+3) - 7^(5n+3) + 3 * 7^(4n+2) - 7^(3n+2) + 3 * 7^(2n+1) - 7^(n+1) + 1.

Aurifeuillian factorization: 7^(14n+7) + 1 = (7^(2n+1) + 1) * a(n) * A220984(n).

G.f.: -(184010736563880737*x^6 +268740854387875086*x^5 +14564007567924591*x^4 [phone]*x^3 [phone]*x^2 [phone]*x +113) / ((x -1)*(7*x -1)*(49*x -1)*(343*x -1)*(2401*x -1)*(16807*x -1)*(117649*x -1)). [Colin Barker, Jan 04 2013]