A320772 Prime generating polynomial: a(n) = (4*n - 29)^2 + 58.

683, 499, 347, 227, 139, 83, 59, 67, 107, 179, 283, 419, 587, 787, 1019, 1283, 1579, 1907, 2267, 2659, 3083, 3539, 4027, 4547, 5099, 5683, 6299, 6947, 7627, 8339, 9083, 9859, 10667, 11507, 12379, 13283, 14219, 15187, 16187, 17219, 18283, 19379, 20507, 21667, 22859, 24083, 25339, 26627, 27947

Offset

1,1

Comments

The polynomial (4*n - 29)^2 + 58 generates 28 distinct primes in succession from n=1 to 28.

Links

Table of n, a(n) for n=1..49.

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

Formula

From Elmo R. Oliveira, Feb 08 2025: (Start)

G.f.: x*(899*x^2 - 1550*x + 683)/(1-x)^3.

E.g.f.: exp(x)*(16*x^2 - 216*x + 899) - 899.

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

Mathematica

Array[(4# - 29)^2 + 58 &, 50] (* Amiram Eldar, Dec 15 2018 *)

Crossrefs

Cf. A048988.

Sequence in context: A145321 A175155 A174105 * A045154 A300193 A234502

Adjacent sequences: A320769 A320770 A320771 * A320773 A320774 A320775

Keyword

nonn,easy,changed

Author

Arashdeep Singh, Oct 21 2018

Status

approved