A214732 a(n) = 25*n^2 + 15*n + 1021.

1021, 1061, 1151, 1291, 1481, 1721, 2011, 2351, 2741, 3181, 3671, 4211, 4801, 5441, 6131, 6871, 7661, 8501, 9391, 10331, 11321, 12361, 13451, 14591, 15781, 17021, 18311, 19651, 21041, 22481, 23971, 25511, 27101, 28741, 30431, 32171, 33961, 35801, 37691

Offset: 0

Author

Robert Potter, Jul 27 2012

Keywords

• nonn
• easy

Comments

This is the case m=5 and k=41 of the formula m^2*n^2 + (m^2 - 2*m)*n + (m^2*k) - (m-1). The most famous example is when m=1 and k=41 (Euler's generating polynomial). With k=41 the formula gives consecutive primes for m=10 and n=0..10, m=17 and n=0..10, m=86 and n=0..8. It is interesting to note that the sequences produced are all factors of the semiprimes produced by m=1, k=41. The other famous values to try for k are 5, 11 and 17 as these all produce primes up to k^2.

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. A215814.

Programs

Magma

[25*n^2+15*n+1021: n in [0..40]] // Vincenzo Librandi, Aug 29 2012

Maple

A214732:= n-> 25*n^2 +15*n +1021; seq(A214732(n), n=0..40); # G. C. Greubel, Apr 26 2021

Mathematica

Table[25n^2 +15n +1021, {n, 0, 40}] (* Vincenzo Librandi, Aug 29 2012 *)
LinearRecurrence[{3,-3,1},{1021,1061,1151},40] (* Harvey P. Dale, May 31 2025 *)

PARI

a(n)=25*n^2+15*n+1021 \\ Charles R Greathouse IV, Oct 25 2012

Sage

[25*n^2 +15*n +1021 for n in (0..40)] # G. C. Greubel, Apr 26 2021

Formula

G.f.: (1021-2002*x+1031*x^2)/(1-x)^3. - Bruno Berselli, Aug 28 2012

E.g.f.: (1021 + 40*x + 25*x^2)*exp(x). - G. C. Greubel, Apr 26 2021