A247010 Primes p such that (p-3)/2 and 2*p+3 are both prime.

7, 13, 17, 29, 89, 97, 137, 197, 229, 277, 337, 349, 397, 557, 617, 797, 929, 937, 1117, 1217, 1237, 1777, 2129, 2309, 2437, 2477, 2617, 2749, 2857, 2909, 3049, 3109, 3137, 3329, 3389, 4057, 4229, 4289, 4409, 5237, 5297, 5417, 5557, 5717, 5857, 6689

Offset: 1

Author

Vincenzo Librandi, Sep 09 2014

Keywords

• nonn
• easy
• less

Comments

A023204 INTERSECT A089531. After 7, all terms are obviously in A002144.

Conjecture: the sequence is infinite.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A023204, A023242, A089531.

Programs

Magma

[p: p in PrimesUpTo(7000) | IsPrime((p-3)div 2) and IsPrime(2*p+3)];

Mathematica

Select[Prime[Range[900]], And@@PrimeQ/@{(# - 3)/2, 2 # + 3} &]

PARI

is(n)=isprime(n) && isprime(2*n+3) && isprime((n-3)\2) \\ Charles R Greathouse IV, Sep 09 2014

Sage

def t(i): return 2*i+3
[t(p) for p in primes(5000) if is_prime(t(p)) and is_prime(t(t(p)))] # Bruno Berselli, Sep 09 2014

Formula

a(n) = 2*A023242(n) + 3. [Bruno Berselli, Sep 09 2014]