A236467 Primes p with p + 2 and prime(p) - 2 both prime.

3, 11, 29, 149, 179, 191, 269, 347, 431, 461, 617, 659, 1031, 1619, 1931, 3467, 3527, 4799, 6569, 6689, 7349, 7877, 9011, 9767, 11117, 12611, 13691, 13901, 14549, 16067, 16139, 16451, 16631, 17489, 17681, 18911, 20981, 22367, 23909, 24179

Offset

1,1

Comments

According to the conjecture in A236468, this sequence should have infinitely many terms.

See A236457 and A236458 for similar sequences.

Links

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

Example

a(1) = 3 since 3, 3 + 2 = 5 and prime(3) - 2 = 3 are all prime, but 2 + 2 = 4 is composite.

Mathematica

p[n_]:=p[n]=PrimeQ[n+2]&&PrimeQ[Prime[n]-2]
n=0; Do[If[p[Prime[m]], n=n+1; Print[n, " ", Prime[m]]], {m, 1, 10000}]
Select[Prime[Range[3000]], AllTrue[{#+2, Prime[#]-2}, PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 11 2020 *)

Crossrefs

Cf. A000040, A001359, A006512, A236119, A236457, A236458, A236462, A236464, A236468.

Sequence in context: A122023 A259594 A293010 * A328550 A179234 A338051

Adjacent sequences: A236464 A236465 A236466 * A236468 A236469 A236470

Keyword

nonn

Author

Zhi-Wei Sun, Jan 26 2014

Status

approved