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

Author

Alexei Kourbatov, Dec 09 2013

Keywords

• nonn

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.

Examples

			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.
		

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

Crossrefs

Cf. A022008, A200503, A200504.

Formula

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