A200504 Initial primes in prime sextuplets (p, p+4, p+6, p+10, p+12, p+16) preceding the maximal gaps in A200503.

7, 97, 19417, 43777, 3400207, 11664547, 37055647, 82984537, 89483827, 94752727, 381674467, 1569747997, 2019957337, 5892947647, 6797589427, 14048370097, 23438578897, 24649559647, 29637700987, 29869155847, 45555183127, 52993564567, 58430706067, 93378527647

Offset: 1

Author

Alexei Kourbatov, Nov 18 2011

Keywords

• nonn
• hard

Comments

Prime sextuplets (p, p+4, p+6, p+10, p+12, p+16) are densest permissible constellations of 6 primes. The maximal 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)=7. The gap of 15960 between sextuplets starting at p=97 and p=16057 is a maximal gap - larger than any preceding gap; so a(2)=97. The next gap is smaller, so 16057 is not in A200504. The gap of 24360 after the sextuplet starting at p=19417 is a maximal gap, therefore a(3)=19417; and so on.
		

Links

• Alexei Kourbatov, Table of n, a(n) for n = 1..56
• Tony Forbes, List of all possible patterns of prime k-tuplets (up to k=50)
• Alexei Kourbatov, Maximal gaps between prime k-tuples
• Alexei Kourbatov and Marek Wolf, Predicting maximal gaps in sets of primes, arXiv preprint arXiv:1901.03785 [math.NT], 2019.

Crossrefs

Cf. A022008 (prime sextuplets), A200503, A233426.