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A133123 Double Sophie Germain semiprimes: semiprimes s such that s1=2s+1 and s2=2s1+1 are also semiprimes.

%I A133123 #7 Mar 18 2019 21:46:42
%S A133123 38,46,106,129,133,145,169,201,203,235,289,291,298,334,335,381,407,
%T A133123 417,458,489,497,529,538,579,583,597,623,626,649,685,689,694,707,758,
%U A133123 767,781,815,898,899,921,926,959,995,1073,1079,1082,1094,1099,1139,1142
%N A133123 Double Sophie Germain semiprimes: semiprimes s such that s1=2s+1 and s2=2s1+1 are also semiprimes.
%C A133123 Numbers n such that both n and 2n+1 are in A111153.
%C A133123 If 29+30*k, 39+40*k and 47+48*k are all primes then 58+60*k is in the sequence.  Thus Dickson's conjecture implies this sequence is infinite. - _Robert Israel_, Mar 17 2019
%H A133123 Robert Israel, <a href="/A133123/b133123.txt">Table of n, a(n) for n = 1..10000</a>
%F A133123 n, n1=2n+1 and n2=2n1+1 are semiprimes.
%e A133123 38=2*19, 2*38+1=77=7*11 and 2*77+1=155=5*31;
%e A133123 129=3*43, 2*129+1=259=7*37 and 2*259+1=519=3*173.
%p A133123 filter:= n -> andmap(numtheory:-bigomega=2, [n,2*n+1,4*n+3]):
%p A133123 select(filter, [$1..2000]); # _Robert Israel_, Mar 17 2019
%t A133123 fQ[n_]:=2==Plus@@Last/@FactorInteger[n];Select[Range[2000],fQ[ # ]&&fQ[2#+1]&&fQ[4#+3]&]
%Y A133123 Cf. A111153.
%K A133123 nonn
%O A133123 1,1
%A A133123 _Zak Seidov_, Sep 19 2007