A201599 Initial primes in prime triples (p, p+2, p+6) preceding the maximal gaps in A201598.

5, 17, 41, 107, 347, 461, 881, 1607, 2267, 2687, 6197, 6827, 39227, 46181, 56891, 83267, 167621, 375251, 381527, 549161, 741677, 805031, 931571, 2095361, 2428451, 4769111, 4938287, 12300641, 12652457, 13430171, 14094797, 18074027, 29480651, 107379731, 138778301, 156377861

Offset

1,1

Comments

Prime triples (p, p+2, 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 A201598; see more comments there.

Links

Alexei Kourbatov, Table of n, a(n) for n = 1..72

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 [math.NT], 2013.

Alexei Kourbatov and Marek Wolf, Predicting maximal gaps in sets of primes, arXiv preprint arXiv:1901.03785 [math.NT], 2019.

Eric W. Weisstein, k-Tuple Conjecture

Example

The gap of 6 between triples starting at p=5 and p=11 is the very first gap, so a(1)=5. The gap of 6 between triples starting at p=11 and p=17 is not a record, so it does not contribute to the sequence. The gap of 24 between triples starting at p=17 and p=41 is a maximal gap - larger than any preceding gap; therefore a(2)=17.

Crossrefs

Cf. A022004 (prime triples p, p+2, p+6), A201598.

Sequence in context: A086499 A097123 A139562 * A246636 A146794 A146834

Adjacent sequences: A201596 A201597 A201598 * A201600 A201601 A201602

Keyword

nonn

Author

Alexei Kourbatov, Dec 03 2011

Status

approved