|
%I #17 Feb 24 2023 16:27:50
%S 2,6,7,11,12,17,18,27,29,35,37,42,43,48,51,53,54,55,60,65,66,69,72,73,
%T 75,79,83,84,87,90,93,97,115,119,125,132,133,135,137,141,144,150,153,
%U 155,159,161,165,169,174,183,186,187,189,191,192,195,198
%N Numbers k such that k^2 + 2 is a semiprime.
%C The semiprimes of this form are: 6, 38, 51, 123, 146, 291, 326, 731, 843, 1227, 1371, 1766, 1851, 2306, 2603, 2811, 2918, 3027, 3602, ....
%C There are no four consecutive terms in this sequence, that is, a(n) > a(n-3) + 3 (check mod 6). Probably sieve theory can show that this sequence has density 0. - _Charles R Greathouse IV_, Feb 24 2023
%H Vincenzo Librandi, <a href="/A242330/b242330.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) > 2n for n > 1. - _Charles R Greathouse IV_, Feb 24 2023
%t Select[Range[300], PrimeOmega[#^2 + 2] == 2 &]
%o (Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [2..200] | IsSemiprime(s) where s is n^2+2];
%o (PARI) issemi(n)=forprime(p=2,997,if(n%p==0, return(isprime(n/p)))); bigomega(n)==2
%o is(n)=issemi(n^2+2) \\ _Charles R Greathouse IV_, Feb 24 2023
%Y Cf. A056899, A067201, A085722, A242331, A242332, A242333.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, May 14 2014
|
