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URL: https://oeis.org/A048058

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A048058
a(n) = n^2 + n + 11.
15
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
P. A. Fontebasso, Un'altra formula che dà una serie limitata di numeri primi, Supplemento al Periodico di matematica (1899), p. 130.
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
KEYWORD
nonn,easy
STATUS
approved