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Numbers that are both Sophie Germain semiprimes and semi-Sophie Germain semiprimes.
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%I #12 May 10 2020 04:26:48

%S 4,10,25,46,55,106,123,145,159,205,226,267,339,358,415,466,529,573,

%T 583,718,753,843,865,979,1077,1195,1243,1257,1293,1366,1405,1465,1473,

%U 1486,2098,2157,2206,2427,2455,2545,2563,2581,2599,2629,2809,2818,2998,3057

%N Numbers that are both Sophie Germain semiprimes and semi-Sophie Germain semiprimes.

%C This is the intersection of the sequence of Sophie Germain semiprimes (A111153) and semi-Sophie Germain semiprimes (A111206).

%H Amiram Eldar, <a href="/A111207/b111207.txt">Table of n, a(n) for n = 1..10000</a>

%e a(4)=46 because 46 is the 4th semiprime such that 2*46+1=93 is a semiprime and both of its factors are Sophie Germain primes: 2*2+1=5 and 2*23+1=47.

%t seqQ[n_] := AllTrue[{n, 2*n + 1}, PrimeOmega[#] == 2 &] && AllTrue[First /@ FactorInteger[n], PrimeQ[2*# + 1] &]; Select[Range[3000], seqQ] (* _Amiram Eldar_, May 10 2020 *)

%Y Cf. A111153, A001358, A005384, A111206.

%K nonn

%O 1,1

%A Christopher M. Tomaszewski (cmt1288(AT)comcast.net), Oct 24 2005

%E Extended by _Ray Chandler_, Oct 31 2005