A168163 Sophie Germain primes p such that the concatenation of p and 2p+1 is again prime.

3, 11, 23, 113, 173, 281, 359, 431, 491, 509, 719, 1103, 1229, 1559, 1889, 1931, 2039, 2393, 2459, 3413, 3539, 3761, 3911, 4391, 4793, 5303, 6113, 6263, 6329, 6491, 6563, 7643, 7823, 7883, 8069, 8093, 8951, 9221, 9473, 10061, 10091, 10589, 10781, 11369

Offset

1,1

Comments

A subsequence of A005384 (Sophie Germain primes: 2p+1 is prime) and of A168164 (which does not require 2p+1 to be prime).

The primes concat(p,2p+1) are listed in A168165.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Mathematica

sgp2Q[p_]:=Module[{s=2p+1}, AllTrue[{s, p 10^IntegerLength[s]+s}, PrimeQ]]; Select[ Prime[ Range[ 1500]], sgp2Q] (* Harvey P. Dale, Jul 11 2023 *)

Prog

(PARI) forprime(p=1, 19999, isprime(2*p+1) & isprime(eval(Str(p, 2*p+1))) & print1(p", "))

Crossrefs

Sequence in context: A002515 A096297 A081857 * A120088 A081737 A005475

Adjacent sequences: A168160 A168161 A168162 * A168164 A168165 A168166

Keyword

base,nonn

Author

M. F. Hasler, Nov 25 2009

Status

approved