A118479 Least n-digit prime which is also a twin prime and Sophie Germain prime.

3, 11, 179, 1019, 10091, 100361, 1000211, 10001399, 100001651, 1000002359, 10000003001, 100000026569, 1000000000061, 10000000019759, 100000000018109, 1000000000029911, 10000000000013741, 100000000000004381

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..100

Example

3 and 5 are twin primes and 2*3+1=7 is prime, so 3 is the first of twin primes and is a Sophie Germain prime; it is the least such 1-digit prime, so a(1)=3.
11 and 13 are twin primes and 2*11+1=23 is prime, so 11 is the first of twin primes and is a Sophie Germain prime; it is the least such 2-digit prime, so a(2)=11.

Mathematica

f[n_] := Block[{k = 10^(n - 1)}, While[ !PrimeQ[k] || !PrimeQ[k + 2] || !PrimeQ[2k + 1], k++ ]; k]; Array[f, 18] (* Robert G. Wilson v, May 13 2006 *)
lndp[n_]:=Module[{p=NextPrime[10^n]}, While[NoneTrue[p+{2, -2}, PrimeQ] || !PrimeQ[2p+1], p=NextPrime[p]]; p]; Array[ lndp, 20, 0] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 06 2019 *)

Crossrefs

Cf. A001359, A005384.

Sequence in context: A006485 A003115 A053888 * A103836 A284704 A081484

Adjacent sequences: A118476 A118477 A118478 * A118480 A118481 A118482

Keyword

nonn,base

Author

Pierre CAMI, May 05 2006

Extensions

Edited by Robert G. Wilson v, May 13 2006

Status

approved