A110581 Primes p such that 2p-1 is prime, but 4p-3 is not prime.

3, 7, 31, 37, 97, 139, 157, 199, 211, 229, 271, 307, 337, 367, 379, 547, 577, 601, 607, 661, 691, 727, 811, 877, 937, 967, 997, 1009, 1171, 1237, 1297, 1399, 1429, 1459, 1609, 1627, 1657, 1759, 1867, 2011, 2029, 2137, 2221, 2281, 2467, 2539, 2551, 2557

Offset: 1

Author

T. D. Noe, Jul 28 2005

Keywords

• nonn
• easy

Comments

A subsequence of A005382, primes p such that 2p-1 is also prime. Note that for all n, 2a(n)-1 is not in this sequence.

Links

• T. D. Noe, Table of n, a(n) for n=1..1000
• Jeffery J. Holt, The minimal number of solutions to phi(n)=phi(n+k), Math. Comp., 72 (2003), 2059-2061.

Programs

Magma

[p: p in PrimesUpTo(2600) | IsPrime(2*p-1) and not IsPrime(4*p-3)]; // Vincenzo Librandi, Apr 14 2013

Mathematica

Select[Prime[Range[2, 1000]], PrimeQ[2#-1] && !PrimeQ[4#-3]&]