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

1,1

Comments

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A111153, A001358, A005384, A111206.

Sequence in context: A265438 A145368 A266826 * A298018 A254233 A300760

Adjacent sequences: A111204 A111205 A111206 * A111208 A111209 A111210

Keyword

nonn

Author

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

Extensions

Extended by Ray Chandler, Oct 31 2005

Status

approved