A236568 Primes p with prime(p + 2) + 2 prime.

3, 5, 11, 31, 41, 43, 47, 67, 79, 107, 199, 223, 251, 263, 311, 313, 461, 467, 499, 577, 599, 641, 727, 743, 797, 911, 919, 929, 1163, 1187, 1277, 1303, 1429, 1433, 1447, 1613, 1619, 1621, 1637, 1783, 1789, 1823, 1831, 1867, 1879, 1997, 2029, 2039, 2089, 2309

Offset: 1

Author

Zhi-Wei Sun, Jan 28 2014

Keywords

• nonn

Comments

This sequence is interesting because of the conjecture in A236566.

Note that A236457 is a subsequence of the sequence.

Examples

			a(1) = 3 since prime(3 + 2) + 2 = 11 + 2 = 13 is prime, but prime (2 + 2) + 2 = 9 is not.
		

Links

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

Crossrefs

Cf. A000040, A001359, A006512, A236457, A236566.

Programs

Mathematica

p[n_]:=PrimeQ[Prime[n+2]+2]
n=0;Do[If[p[Prime[m]],n=n+1;Print[n," ",Prime[m]]],{m,1,10000}]
Select[Prime[Range[400]],PrimeQ[Prime[#+2]+2]&] (* Harvey P. Dale, Feb 13 2024 *)