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

1,1

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.

Links

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

Example

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

Mathematica

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

Crossrefs

Cf. A000040, A001043.

Sequence in context: A072677 A117249 A063910 * A189557 A045444 A129782

Adjacent sequences: A288629 A288630 A288631 * A288633 A288634 A288635

Keyword

nonn

Author

Zak Seidov, Jun 12 2017

Status

approved