A215814 a(n) = 60516*n^2 - 61008*n + 2481403.

2481403, 2480911, 2601451, 2843023, 3205627, 3689263, 4293931, 5019631, 5866363, 6834127, 7922923, 9132751, 10463611, 11915503, 13488427, 15182383, 16997371, 18933391, 20990443, 23168527, 25467643, 27887791, 30428971, 33091183, 35874427, 38778703, 41804011, 44950351

Offset: 0

Author

Robert Potter, Aug 28 2012

Keywords

• nonn
• easy

Comments

The formula gives consecutive primes for n from 1 to 20, except n = 9.

This is the case m = 41*6 = 246 and k = 41 of the polynomial m^2*n^2 + (m^2 - 2*m)*n + (m^2*k) - (m-1).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A214732.

Programs

Magma

[60516*n^2-61008*n+2481403: n in [0..26]]; // Bruno Berselli, Aug 28 2012

Maple

A215814:=n->60516*n^2 - 61008*n + 2481403; seq(A215814(n), n=0..100); # Wesley Ivan Hurt, Nov 28 2013

Mathematica

Table[60516 n^2 - 61008 n + 2481403, {n, 0, 30}] (* Vincenzo Librandi, Aug 29 2012 *)

PARI

a(n)=60516*n^2-61008*n+2481403 \\ Charles R Greathouse IV, Jun 17 2017

Formula

G.f.: (2481403 - 4963298*x + 2602927*x^2)/(1-x)^3. - Bruno Berselli, Aug 28 2012

From Elmo R. Oliveira, Feb 09 2025: (Start)

E.g.f.: exp(x)*(2481403 - 492*x + 60516*x^2).

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

Extensions

Offset changed from 1 to 0 and a(0) added from Vincenzo Librandi, Aug 29 2012

Gf adapted to the offset by Bruno Berselli, Aug 29 2012