A023228 Numbers k such that k and 8*k + 1 are both prime.

2, 5, 11, 17, 29, 71, 101, 107, 131, 137, 149, 179, 239, 269, 347, 401, 431, 449, 479, 491, 509, 557, 599, 617, 659, 677, 761, 809, 821, 857, 929, 941, 947, 977, 1151, 1187, 1229, 1289, 1307, 1361, 1367, 1409, 1487, 1559, 1571, 1601, 1619, 1667, 1697, 1811, 1871

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Samuel S. Wagstaff, Jr., Sum of Reciprocals of Germain Primes, Journal of Integer Sequences, Vol. 24, No. 2 (2021), Article 21.9.5.

Crossrefs

Cf. A007519 (primes of form 8n+1), A005123 ((( primes == 1 mod 8 ) - 1)/8). - Klaus Brockhaus, Dec 21 2008

Programs

Magma

[ p: p in PrimesUpTo(1900) | IsPrime(8*p+1) ]; // Klaus Brockhaus, Dec 21 2008

Mathematica

Select[Prime[Range[2000]], PrimeQ[8# + 1]&] (* Vincenzo Librandi, Feb 02 2014 *)

PARI

list(lim)=my(v=List()); forprime(p=2,lim, if(isprime(8*p+1), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Oct 20 2021

Formula

Sum_{n>=1} 1/a(n) is in the interval (1.151956749, 1.4207187) (Wagstaff, 2021). - Amiram Eldar, Nov 04 2021