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

Author

Zhi-Wei Sun, Jan 26 2014

Keywords

• nonn

Comments

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

See A236457 and A236458 for similar sequences.

Examples

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

Links

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

Crossrefs

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

Programs

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 *)