

A228183


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


8



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
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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 bfile: *) 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 A322745 A189654
Adjacent sequences: A228180 A228181 A228182 * A228184 A228185 A228186


KEYWORD

nonn,less


AUTHOR

Shyam Sunder Gupta, Aug 15 2013


STATUS

approved



