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

1,1

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

Formula

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

Mathematica

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

Prog

(Magma) [p: p in PrimesUpTo(7000) | IsPrime((p-3)div 2) and IsPrime(2*p+3)];
(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
(PARI) is(n)=isprime(n) && isprime(2*n+3) && isprime((n-3)\2) \\ Charles R Greathouse IV, Sep 09 2014

Crossrefs

Cf. A023204, A023242, A089531.

Sequence in context: A181570 A154408 A089531 * A138337 A359063 A174877

Adjacent sequences: A247007 A247008 A247009 * A247011 A247012 A247013

Keyword

nonn,easy,less

Author

Vincenzo Librandi, Sep 09 2014

Status

approved