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A111207 Numbers that are both Sophie Germain semiprimes and semi-Sophie Germain semiprimes. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 29 05:48 EDT 2020. Contains 337425 sequences. (Running on oeis4.)