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A236457
Primes p with q = p + 2 and prime(q) + 2 both prime.
12
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.
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
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Jan 26 2014
STATUS
approved