A288632 Primes p such that (p+q)/6 is prime, q is the next prime after p.

5, 7, 13, 19, 37, 67, 89, 109, 127, 307, 379, 389, 449, 487, 499, 683, 719, 769, 877, 929, 937, 1009, 1163, 1297, 1523, 1559, 1567, 1831, 1933, 1979, 2153, 2213, 2221, 2269, 2389, 2459, 2659, 2803, 2857, 2909, 3037, 3089

Offset: 1

Author

Zak Seidov, Jun 12 2017

Keywords

• nonn

Comments

Among first 2*10^6 primes there are 61953 terms of the sequence; e.g., a(60000)=31320053 and (31320053+31320061)/6=10440019=A000040(691876).

Except for the case 7-5=2 the minimal value of first differences is 4.

Examples

			5+7=6*2, 7+11=6*3, 13+17=6*5, 19+23=6*7, 37+41=6*11, 67+71=6*23.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001043.

Programs

Mathematica

Select[Prime[Range[1000]], PrimeQ[(# + NextPrime[#])/6] &]