A258841 a(n) = 9*n^2 - 237*n + 1927.

1927, 1699, 1489, 1297, 1123, 967, 829, 709, 607, 523, 457, 409, 379, 367, 373, 397, 439, 499, 577, 673, 787, 919, 1069, 1237, 1423, 1627, 1849, 2089, 2347, 2623, 2917, 3229, 3559, 3907, 4273, 4657, 5059, 5479, 5917, 6373, 6847, 7339, 7849, 8377, 8923, 9487, 10069

Offset

0,1

Comments

Empirical observation. All integers generated by polynomial for 0 < n <= 37 are prime with the exception of a(26) = 43^2 and a(29) = 43*61.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Prime-Generating Polynomial.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

From Vincenzo Librandi, Jun 22 2015: (Start)

G.f.: (1927 - 4082*x + 2173*x^2)/(1-x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)

E.g.f.: exp(x)*(1927 - 228*x + 9*x^2). - Elmo R. Oliveira, Feb 09 2025

Mathematica

Table[9 n^2 - 237 n + 1927, {n, 0, 25}] (* Michael De Vlieger, Jun 12 2015 *)
LinearRecurrence[{3, -3, 1}, {1927, 1699, 1489}, 50] (* Harvey P. Dale, Oct 08 2024 *)

Prog

(PARI) vector(50, n, 9*n^2 - 237*n + 1927) \\ Michel Marcus, Jun 21 2015
(Magma) [9*n^2-237*n+1927: n in [0..50]]; // Vincenzo Librandi, Jun 22 2015

Crossrefs

Cf. A202018, A214732, A215814.

Sequence in context: A202051 A283949 A133301 * A099482 A253337 A200435

Adjacent sequences: A258838 A258839 A258840 * A258842 A258843 A258844

Keyword

nonn,easy,less

Author

Robert Potter, Jun 12 2015

Status

approved