A345735 A prime-generating quasipolynomial: a(n) = 6*floor(n^2/4) + 17.

17, 17, 23, 29, 41, 53, 71, 89, 113, 137, 167, 197, 233, 269, 311, 353, 401, 449, 503, 557, 617, 677, 743, 809, 881, 953, 1031, 1109, 1193, 1277, 1367, 1457, 1553, 1649, 1751, 1853, 1961, 2069, 2183, 2297, 2417, 2537, 2663, 2789, 2921, 3053, 3191, 3329, 3473, 3617

Offset

0,1

Comments

Fontebasso only claims that the terms are prime from 0 to 22, but in fact a(23)..a(30) are all prime as well. The first composite term is a(31) = 1457 = 31*47.

Links

Table of n, a(n) for n=0..49.

P. A. Fontebasso, Une'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 (2,0,-2,1).

Formula

a(n) = A319127(n+1) + 17 = 6*A002620(n) + 17. - Omar E. Pol, Jul 12 2021

G.f.: (17*x^3-11*x^2-17*x+17)/((x+1)*(1-x)^3). - Alois P. Heinz, Jul 12 2021

E.g.f.: ((34 + 3*x + 3*x^2)*cosh(x) + (31 + 3*x + 3*x^2)*sinh(x))/2. - Stefano Spezia, Jul 13 2021

Prog

(PARI) a(n)=n^2\4*6+17

Crossrefs

Cf. A002620, A319127.

Sequence in context: A216436 A060360 A081702 * A238235 A333152 A040273

Adjacent sequences: A345732 A345733 A345734 * A345736 A345737 A345738

Keyword

nonn,easy

Author

Charles R Greathouse IV, Jun 30 2021

Status

approved