A201597 Initial prime in prime triples (p, p+4, p+6) preceding the maximal gaps in A201596.

7, 13, 37, 103, 307, 457, 613, 2137, 2377, 2797, 3463, 4783, 5737, 9433, 14557, 24103, 45817, 52177, 126487, 317587, 580687, 715873, 2719663, 6227563, 8114857, 10085623, 10137493, 18773137, 21297553, 25291363, 43472497, 52645423, 69718147, 80002627, 89776327

Offset: 1

Author

Alexei Kourbatov, Dec 03 2011

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)=7. The gap of 24 between triples starting at p=13 and p=37 is a maximal gap - larger than any preceding gap; therefore a(2)=13. The gap of 30 between triples at p=37 and p=67 is again a maximal gap, so a(3)=37. The next gap is smaller, so it does not contribute 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 and Marek Wolf, Predicting maximal gaps in sets of primes, arXiv preprint arXiv:1901.03785 [math.NT], 2019.
• Eric W. Weisstein, k-Tuple Conjecture

Crossrefs

Cf. A022005 (prime triples p, p+4, p+6), A201596.

Programs

Mathematica

DeleteDuplicates[{#[[1]],#[[2]]-#[[1]]}&/@Partition[Select[Prime[Range[ 5206000]],AllTrue[#+{4,6},PrimeQ]&],2,1],GreaterEqual[#1[[2]],#2[[2]]]&] [[All,1]] (* Harvey P. Dale, Aug 04 2022 *)