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A177221 Numbers k that are the products of two distinct primes such that 2*k + 1 is also the product of two distinct primes.

%I A177221 #25 Dec 15 2024 17:01:25
%S A177221 10,34,38,46,55,57,77,91,93,106,118,123,129,133,143,145,159,161,177,
%T A177221 185,201,203,205,206,213,218,226,235,259,267,291,295,298,305,314,327,
%U A177221 334,335,339,358,365,377,381,394,395,403,407,415,417,446,447,458,466,469
%N A177221 Numbers k that are the products of two distinct primes such that 2*k + 1 is also the product of two distinct primes.
%H A177221 Robert Israel, <a href="/A177221/b177221.txt">Table of n, a(n) for n = 1..10000</a>
%e A177221 10 is in the sequence because 10 = 2*5 and 2*10+1 = 21 = 3*7.
%p A177221 isA006881:= proc(n) local F;
%p A177221   F:= ifactors(n)[2];
%p A177221   nops(F)=2 and F[1, 2]+F[2, 2]=2
%p A177221 end proc:
%p A177221 filter:= n -> andmap(isA006881, [n, 2*n+1]); select(filter, [$1..1000]); # _Robert Israel_, Nov 09 2017
%t A177221 f[n_]:=Last/@FactorInteger[n]=={1,1}; lst={};Do[If[f[n]&&f[2*n+1],AppendTo[lst,n]],{n,0,3*6!}];lst
%t A177221 Select[Range[500],PrimeNu[#]==PrimeOmega[#]==PrimeNu[2#+1] == PrimeOmega[ 2#+1] == 2&] (* _Harvey P. Dale_, Feb 22 2018 *)
%Y A177221 Cf. A006881, A111153, A177210, A177211, A177212, A177213, A177214, A177215, A177216, A177217, A177220.
%K A177221 nonn
%O A177221 1,1
%A A177221 _Vladimir Joseph Stephan Orlovsky_, May 05 2010