A048058 a(n) = n^2 + n + 11.

11, 13, 17, 23, 31, 41, 53, 67, 83, 101, 121, 143, 167, 193, 221, 251, 283, 317, 353, 391, 431, 473, 517, 563, 611, 661, 713, 767, 823, 881, 941, 1003, 1067, 1133, 1201, 1271, 1343, 1417, 1493, 1571, 1651, 1733, 1817, 1903, 1991, 2081, 2173, 2267, 2363, 2461, 2561

Offset

0,1

Comments

Fontebasso lists this as a prime-generating polynomial due to Legendre, but doesn't give a reference. - Charles R Greathouse IV, Jun 30 2021

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

P. A. Fontebasso, Un'altra formula che dà una serie limitata di numeri primi, Supplemento al Periodico di matematica (1899), p. 130.

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

Formula

For n > 4: a(n) = A176271(n+1,6). - Reinhard Zumkeller, Apr 13 2010

a(n) = 2*n + a(n-1) (with a(0)=11). - Vincenzo Librandi, Aug 06 2010

Sum_{n>=0} 1/a(n) = Pi*tanh(Pi*sqrt(43)/2)/sqrt(43). - Amiram Eldar, Jan 17 2021

From Elmo R. Oliveira, Oct 28 2024: (Start)

G.f.: (11 - 20*x + 11*x^2)/(1 - x)^3.

E.g.f.: (11 + 2*x + x^2)*exp(x).

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

Maple

with(combinat):seq(fibonacci(3, n)+n+10, n=0..45); # Zerinvary Lajos, Jun 07 2008

Mathematica

f[n_]:=n^2+n+11; f[Range[0, 100]] (* Vladimir Joseph Stephan Orlovsky, Mar 12 2011*)

Prog

(PARI) a(n)=n^2+n+11 \\ Charles R Greathouse IV, Jun 29 2015

Crossrefs

Cf. A002522, A048059, A048097, A176271.

Sequence in context: A106891 A191031 A106890 * A048059 A106076 A006489

Adjacent sequences: A048055 A048056 A048057 * A048059 A048060 A048061

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved