A228183 Semiprimes generated by the Euler polynomial x^2 + x + 41.

1681, 1763, 2021, 2491, 3233, 4331, 5893, 6683, 6847, 7181, 7697, 8051, 8413, 9353, 10547, 10961, 12031, 13847, 14803, 15047, 15293, 16043, 16297, 17071, 18673, 19223, 19781, 20633, 21797, 24221, 25481, 26123, 26447, 26773, 27101, 29111, 29797, 30143

Offset: 1

Author

Shyam Sunder Gupta, Aug 15 2013

Keywords

• nonn
• less

Comments

This is a subsequence of A145292. The first numbers in A145292 but not in here are 176861, 186233, 241613, 242597, ...

Examples

			The semiprime 1763 = 41^2 + 41 + 41 = 41*43 is in the sequence.
		

Links

• Shyam Sunder Gupta and K. D. Bajpai, Table of n, a(n) for n = 1..10000 (first 4760 terms from Shyam Sunder Gupta)

Crossrefs

Cf. A001358, A145292.

Programs

Magma

IsSemiprime:=func; [s: x in [2..200] | IsSemiprime(s) where s is x^2+x+41]; // Bruno Berselli, Aug 15 2013

Mathematica

a = {}; Do[If[PrimeOmega[x^2 + x + 41] == 2, AppendTo[a, x^2 + x + 41]], {x, 1, 200}]; a
(* For the b-file: *) n = 0; Do[t = k^2 + k + 41; If[PrimeOmega[t] == 2, n++; Print[n, " ", t]], {k, 30000}] (* K. D. Bajpai, Apr 22 2014 *)