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

Author

Robert Potter, Jun 12 2015

Keywords

• nonn
• easy
• less

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).

Crossrefs

Cf. A202018, A214732, A215814.

Programs

Magma

[9*n^2-237*n+1927: n in [0..50]]; // Vincenzo Librandi, Jun 22 2015

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 *)

PARI

vector(50, n, 9*n^2 - 237*n + 1927) \\ Michel Marcus, Jun 21 2015

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