|
%I #24 Sep 08 2022 08:46:05
%S 1681,1763,2021,2491,3233,4331,5893,6683,6847,7181,7697,8051,8413,
%T 9353,10547,10961,12031,13847,14803,15047,15293,16043,16297,17071,
%U 18673,19223,19781,20633,21797,24221,25481,26123,26447,26773,27101,29111,29797,30143
%N Semiprimes generated by the Euler polynomial x^2 + x + 41.
%C This is a subsequence of A145292. The first numbers in A145292 but not in here are 176861, 186233, 241613, 242597, ...
%H Shyam Sunder Gupta and K. D. Bajpai, <a href="/A228183/b228183.txt">Table of n, a(n) for n = 1..10000</a> (first 4760 terms from Shyam Sunder Gupta)
%e The semiprime 1763 = 41^2 + 41 + 41 = 41*43 is in the sequence.
%t a = {}; Do[If[PrimeOmega[x^2 + x + 41] == 2, AppendTo[a, x^2 + x + 41]], {x, 1, 200}]; a
%t (* 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 *)
%o (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
%Y Cf. A001358, A145292.
%K nonn,less
%O 1,1
%A _Shyam Sunder Gupta_, Aug 15 2013
|
