A171162 Define Sophie Germain isolated primes to be primes p such that 2p+1 is also prime and so that p-2 and p+2 are not primes. The sequence contains Sophie Germain isolated primes p such that the previous prime to p and the succeeding prime to p are both also Sophie Germain isolated primes.

103619, 145109, 291503, 356591, 362759, 367733, 475523, 521831, 527123, 603191, 609809, 691979, 726419, 810809, 812939, 825491, 940421, 998213, 1117793, 1132811, 1231889, 1329143, 1331789, 1433891, 1433903, 1549403, 1623059

Offset

1,1

Links

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

Mathematica

f[n_]:=PrimeQ[2*n+1]&&!PrimeQ[n-2]&&!PrimeQ[n+2]; PrimeNext[n_]:=Module[{k}, k=n+1; While[ !PrimeQ[k], k++ ]; k]; PrimePrev[n_]:=Module[{k}, k=n-1; While[ !PrimeQ[k], k-- ]; k]; lst={}; Do[p=Prime[n]; If[f[p], If[f[PrimePrev[p]]&&f[PrimeNext[p]], AppendTo[lst, p]]], {n, 9!}]; lst
sgpQ[n_]:=Module[{nxt=NextPrime[n], prev=NextPrime[n, -1]}, AllTrue[{2n+1, 2nxt+1, 2prev+1}, PrimeQ]&&!PrimeQ[n+2]&&!PrimeQ[n-2]&&!PrimeQ[nxt+2] && !PrimeQ[nxt-2]&&!PrimeQ[prev+2]&&!PrimeQ[prev-2]]; Select[Prime[ Range[ 400000]], sgpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 21 2017 *)
Select[Partition[Prime[Range[100000]], 5, 1], Min[ Differences[#]]> 2 && AllTrue[ 2*#[[2;; 4]]+1, PrimeQ]&][[All, 3]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 22 2017 *)

Crossrefs

Cf. A005384, A007510, A130286

Sequence in context: A147526 A269218 A237894 * A235721 A210180 A136312

Adjacent sequences: A171159 A171160 A171161 * A171163 A171164 A171165

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 04 2009

Extensions

Definition rewritten by Harvey P. Dale, Feb 21 2017

Status

approved