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

1,1

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.

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A338812 A052378 A090607 * A158375 A144729 A123250

Adjacent sequences: A201594 A201595 A201596 * A201598 A201599 A201600

Keyword

nonn

Author

Alexei Kourbatov, Dec 03 2011

Status

approved