A233426 Primes p in prime sextuplets (p, p+4, p+6, p+10, p+12, p+16) at the end of the maximal gaps in A200503.

97, 16057, 43777, 1091257, 6005887, 14520547, 40660717, 87423097, 94752727, 112710877, 403629757, 1593658597, 2057241997, 5933145847, 6860027887, 14112464617, 23504713147, 24720149677, 29715350377, 29952516817, 45645253597, 53086708387, 58528934197, 93495691687, 97367556817

Offset

1,1

Comments

Prime sextuplets (p, p+4, p+6, p+10, p+12, p+16) are densest permissible constellations of 6 primes. Maximal (record) gaps between prime sextuplets are listed in A200503; see further comments there.

Links

Alexei Kourbatov, Table of n, a(n) for n = 1..56

Tony Forbes and Norman Luhn, Prime k-tuplets

Alexei Kourbatov, Maximal gaps between prime k-tuples

Alexei Kourbatov, Tables of record gaps between prime constellations, arXiv preprint arXiv:1309.4053, 2013.

Norman Luhn, Record Gaps Between Prime Sextuplets

Eric W. Weisstein, k-Tuple Conjecture

Formula

a(n) = A200504(n) + A200503(n). - Hugo Pfoertner, May 21 2023

Example

Two smallest prime sextuplets (p, p+4, p+6, p+10, p+12, p+16) start at p=7 and p=97; so a[1]=97. The gap of 15960 between sextuplets starting at p=97 and p=16057 is a record gap - larger than any preceding gap; so a[2]=16057. The next gap is not a record, so a new term is not added.

Crossrefs

Cf. A022008, A200503, A200504.

Sequence in context: A218232 A219062 A218318 * A173129 A306480 A321041

Adjacent sequences: A233423 A233424 A233425 * A233427 A233428 A233429

Keyword

nonn

Author

Alexei Kourbatov, Dec 09 2013

Status

approved