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%I #16 Feb 14 2024 02:23:40
%S 113,34925927,4651514210561,556919483179733591,
%T 65684998500756890925713,7730533744900130305342957127,
%U 909535949164303794596648514307361,107006774488854204226839526889653524791,12589253114717671385404089651370543317211313
%N The left Aurifeuillian factor of 7^(14n+7) + 1.
%C The corresponding right Aurifeuillian factor is A220984.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Cunningham_project">Cunningham Project</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (137257, -2354918349, 5670354183893, -1944931485075299, 95029449572634843, -651636050170246351, 558545864083284007).
%F a(n) = 7^(6n+3) - 7^(5n+3) + 3 * 7^(4n+2) - 7^(3n+2) + 3 * 7^(2n+1) - 7^(n+1) + 1.
%F Aurifeuillian factorization: 7^(14n+7) + 1 = (7^(2n+1) + 1) * a(n) * A220984(n).
%F G.f.: -(184010736563880737*x^6 +268740854387875086*x^5 +14564007567924591*x^4 +73553506117028*x^3 +123792021759*x^2 +19415886*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]
%t 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}]
%Y Cf. A092440, A085601, A220978, A198410, A220979-A220990.
%K nonn,easy
%O 0,1
%A _Stuart Clary_, Dec 27 2012