A111207 Numbers that are both Sophie Germain semiprimes and semi-Sophie Germain semiprimes.

4, 10, 25, 46, 55, 106, 123, 145, 159, 205, 226, 267, 339, 358, 415, 466, 529, 573, 583, 718, 753, 843, 865, 979, 1077, 1195, 1243, 1257, 1293, 1366, 1405, 1465, 1473, 1486, 2098, 2157, 2206, 2427, 2455, 2545, 2563, 2581, 2599, 2629, 2809, 2818, 2998, 3057

Offset: 1

Author

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

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A111153, A001358, A005384, A111206.

Programs

Mathematica

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 *)

Extensions

Extended by Ray Chandler, Oct 31 2005