A000355 Primes p == 3, 9, 11 (mod 20) such that 2p+1 is also prime.

3, 11, 23, 29, 83, 89, 131, 191, 251, 431, 443, 491, 509, 683, 743, 809, 911, 1031, 1049, 1103, 1223, 1229, 1289, 1409, 1451, 1511, 1583, 1811, 1889, 1931, 2003, 2063, 2069, 2129, 2351, 2543, 2549, 2903, 2963, 2969, 3023, 3329, 3389, 3449, 3491, 3623, 3803

Offset: 1

Author

Robert A. J. Matthews

Keywords

• nonn
• easy

Comments

a(n) = (A000353(n)-1)/2. - Reinhard Zumkeller, Feb 10 2009

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Robert A. J. Matthews, Maximally periodic reciprocals, Bull. Institute of Mathematics and Its Applications, vol. 28, p. 147-148, 1992.

Crossrefs

Subset of A005384.

Cf. A000353.

Programs

Maple

q:= p-> irem(p, 20) in {3, 9, 11} and andmap(isprime, [p,2*p+1]):
select(q, [$1..10000])[];  # Alois P. Heinz, Oct 31 2023

Mathematica

Select[Prime[Range[1000]], MatchQ[Mod[#, 20], 3|9|11] && PrimeQ[2#+1]&] (* Jean-François Alcover, Feb 07 2016 *)

PARI

is(n)=my(k=n%20); (k==3||k==9||k==11) && isprime(2*n+1) && isprime(n) \\ Charles R Greathouse IV, Nov 20 2014

Extensions

More terms from Reinhard Zumkeller, Feb 10 2009