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

1,1

Comments

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

Links

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

Example

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

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 *)

Prog

(Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [s: x in [2..200] | IsSemiprime(s) where s is x^2+x+41]; // Bruno Berselli, Aug 15 2013

Crossrefs

Cf. A001358, A145292.

Sequence in context: A172667 A221204 A145292 * A175897 A370355 A361705

Adjacent sequences: A228180 A228181 A228182 * A228184 A228185 A228186

Keyword

nonn,less

Author

Shyam Sunder Gupta, Aug 15 2013

Status

approved