|
%I #14 Nov 07 2016 09:23:30
%S 49,65,82,87,91,121,122,123,143,155,159,161,178,185,187,201,205,209,
%T 213,215,217,218,237,249,259,265,278,287,289,291,295,298,299,301,302,
%U 309,314,321,326,327,329,334,361,381,395,407,422,427,445,451,454,466,471
%N Semiprimes n such that n^2+n+41 is also semiprime.
%C n^2+n+41 is sometimes referred to as Euler's polynomial.
%C Subsequence of A228184.
%H K. D. Bajpai, <a href="/A242702/b242702.txt">Table of n, a(n) for n = 1..10000</a>
%e 65 = 5 * 13 is semiprime and 65^2 + 65 + 41 = 4331 = 61 * 71 is also semiprime so 65 is in the sequence.
%e 87 = 3 * 29 is semiprime and 87^2 + 87 + 41 = 7697 = 43 * 179 is also semiprime so 87 is in the sequence.
%e 6 = 2 * 3 is semiprime but 6^2+6+41 = 83 is prime (not semiprime) so 6 is not in the sequence.
%p with(numtheory): A242702:= proc(); if bigomega(n)=2 and bigomega(n^2+n+41)=2 then RETURN (n); fi; end: seq(A242702 (), n=1..1000);
%t c = 0; Do[If [PrimeOmega[n] == 2 && PrimeOmega[n^2 + n + 41] == 2, c++; Print[c, " ", n]], {n, 1, 10^5}];
%t Select[Range[500],PrimeOmega[#]==PrimeOmega[#^2+#+41]==2&] (* _Harvey P. Dale_, Nov 07 2016 *)
%Y Cf. A001358, A228183, A238242, A228184.
%K nonn
%O 1,1
%A _K. D. Bajpai_, May 20 2014
|
