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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 (list; graph; refs; listen; history; text; internal format)
 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:= n=0; Do[If[p[Prime[m]], n=n+1; Print[n, " ", Prime[m]]], {m, 1, 10000}] Select[Prime[Range], 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

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Last modified September 25 05:14 EDT 2021. Contains 347652 sequences. (Running on oeis4.)