A233435 Primes p in prime triples (p, p+4, p+6) at the end of the maximal gaps in A201596.

13, 37, 67, 193, 457, 613, 823, 2377, 2683, 3163, 3847, 5227, 6547, 10267, 15643, 25303, 47143, 54493

Offset: 1

Author

Alexei Kourbatov, Dec 09 2013

Keywords

• nonn

Comments

Prime triples (p, p+4, p+6) are one of the two types of densest permissible constellations of 3 primes. Maximal gaps between triples of this type are listed in A201596; see more comments there.

Examples

			The gap of 6 between triples starting at p=7 and p=13 is the very first gap, so a(1)=13. The gap of 24 between triples starting at p=13 and p=37 is a maximal (record) gap - larger than any preceding gap; therefore a(2)=37. The gap of 30 between triples at p=37 and p=67 is again a record, so a(3)=67. The next gap is smaller, so a new term is not added to the sequence.
		

Links

• Alexei Kourbatov, Table of n, a(n) for n = 1..79
• Tony Forbes, Prime k-tuplets
• Alexei Kourbatov, Maximal gaps between prime triples
• Alexei Kourbatov, Tables of record gaps between prime constellations, arXiv preprint arXiv:1309.4053, 2013.
• Eric W. Weisstein, k-Tuple Conjecture

Crossrefs

Cf. A022005, A201596, A201597.