A318791 Prime generating polynomial: a(n) = 9*n^2 - 249*n + 1763.

1523, 1301, 1097, 911, 743, 593, 461, 347, 251, 173, 113, 71, 47, 41, 53, 83, 131, 197, 281, 383, 503, 641, 797, 971, 1163, 1373, 1601, 1847, 2111, 2393, 2693, 3011, 3347, 3701, 4073, 4463, 4871, 5297, 5741, 6203, 6683, 7181, 7697, 8231, 8783, 9353

Offset: 1

Author

Arashdeep Singh, Dec 15 2018

Keywords

• nonn
• easy

Comments

This polynomial (9*n^2 - 249*n + 1763) generates 40 distinct primes in succession from n = 1 to 40.

Links

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

Crossrefs

Cf. A005846, A007635, A048059, A202018.

Programs

Maple

seq(9*n^2-249*n+1763,n=1..50); # Muniru A Asiru, Dec 19 2018

Mathematica

Array[9#^2 - 249# + 1763 &, 50] (* Amiram Eldar, Dec 15 2018 *)

Formula

From Chai Wah Wu, Feb 12 2019: (Start)

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

G.f.: x*(-1763*x^2 + 3268*x - 1523)/(x - 1)^3. (End)

a(n) = p(41 - 3*n), where p(n) = n^2 + n + 41 is Euler's prime generating polynomial - see A202018 and A005846. - Peter Bala, Jun 10 2021

E.g.f.: exp(x)*(9*x^2 - 240*x + 1763) - 1763. - Elmo R. Oliveira, Feb 10 2025