A118485 a(n) = 11321 - 23479*n + 16423*n^2 - 4693*n^3 + 471*n^4.

43, 47, 131, 397, 12251, 58403, 172867, 400961, 799307, 1435831, 2389763, 3751637, 5623291, 8117867, 11359811, 15484873, 20640107, 26983871, 34685827, 43926941, 54899483, 67807027, 82864451, 100297937, 120344971, 143254343, 169286147

Offset

1,1

Comments

A prime-generating polynomial constructed from a 3 X 3 matrix.

Links

Table of n, a(n) for n=1..27.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

G.f.: -x*(11321*x^4-218*x^3+326*x^2-168*x+43) / (x-1)^5. [Colin Barker, Dec 13 2012]

Mathematica

M = {{0, 1, 0}, {0, 0, 1}, {1, 0, 1}}; v[0] = {41, 43, 47}; v[n_] := v[n] = M.v[n - 1] a = Flatten[Table[If[PrimeQ[Abs[v[n][[1]]]], Abs[v[n][[1]]], {}], {n, 1, 20}]] f[x_] = Expand[InterpolatingPolynomial[a, x]] aout = Table[f[n], {n, 1, 40}]
LinearRecurrence[{5, -10, 10, -5, 1}, {43, 47, 131, 397, 12251}, 30] (* Harvey P. Dale, Aug 01 2021 *)

Crossrefs

Cf. A001608, A000931.

Sequence in context: A033230 A330981 A180519 * A165444 A162464 A255224

Adjacent sequences: A118482 A118483 A118484 * A118486 A118487 A118488

Keyword

nonn,easy

Author

Roger L. Bagula, May 05 2006

Extensions

Edited by N. J. A. Sloane, Jun 26 2009

Status

approved