A236457 Primes p with q = p + 2 and prime(q) + 2 both prime.

3, 5, 11, 41, 107, 311, 461, 599, 641, 1277, 1619, 1997, 2309, 2381, 2789, 3671, 4787, 5099, 6659, 6701, 6827, 7457, 7487, 8219, 8537, 8597, 9929, 10709, 11117, 12071, 12107, 12251, 13709, 17747, 18047, 18251, 18521, 22091, 22637, 23027

Offset

1,1

Comments

According to the conjecture in A236456, this sequence should have infinitely many terms.

See A236458 for a similar sequence.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Example

a(1) = 3 since 3 + 2 = 5 and prime(5) + 2 = 13 are both prime, but 2 + 2 = 4 is not.

Mathematica

p[n_]:=PrimeQ[n+2]&&PrimeQ[Prime[n+2]+2]
In[2]:= n=0; Do[If[p[Prime[m]], n=n+1; Print[n, " ", Prime[m]]], {m, 1, 10000}]
Select[Prime[Range[2600]], AllTrue[{#+2, Prime[#+2]+2}, PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 21 2021 *)

Prog

(PARI) s=[]; forprime(p=2, 24000, q=p+2; if(isprime(q) && isprime(prime(q)+2), s=concat(s, p))); s \\ Colin Barker, Jan 26 2014

Crossrefs

Cf. A000040, A001359, A006512, A236119, A236456, A236458.

Sequence in context: A174915 A162250 A055511 * A105236 A332968 A144467

Adjacent sequences: A236454 A236455 A236456 * A236458 A236459 A236460

Keyword

nonn

Author

Zhi-Wei Sun, Jan 26 2014

Status

approved