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A233435 Primes p in prime triples (p, p+4, p+6) at the end of the maximal gaps in A201596. 2
13, 37, 67, 193, 457, 613, 823, 2377, 2683, 3163, 3847, 5227, 6547, 10267, 15643, 25303, 47143, 54493 (list; graph; refs; listen; history; text; internal format)



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.


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

Eric W. Weisstein, k-Tuple Conjecture


The gap of 6 between triples starting at p=7 and p=13 is the very first gap, so a(1)=13. The gap of 24 between triples starting at p=13 and p=37 is a maximal (record) gap - larger than any preceding gap; therefore a(2)=37. The gap of 30 between triples at p=37 and p=67 is again a record, so a(3)=67. The next gap is smaller, so a new term is not added to the sequence.


Cf. A022005, A201596, A201597.

Sequence in context: A147207 A146877 A309720 * A049742 A347209 A247867

Adjacent sequences: A233432 A233433 A233434 * A233436 A233437 A233438




Alexei Kourbatov, Dec 09 2013



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Last modified December 8 22:05 EST 2022. Contains 358698 sequences. (Running on oeis4.)