A201063 Initial primes in prime 5-tuples (p, p+4, p+6, p+10, p+12) preceding the maximal gaps in A201062.

7, 97, 3457, 5647, 19417, 43777, 101107, 1621717, 3690517, 5425747, 8799607, 9511417, 16388917, 22678417, 31875577, 37162117, 64210117, 119732017, 200271517, 203169007, 241307107, 342235627, 367358347, 378200227

Offset

1,1

Comments

Prime quintuplets (p, p+4, p+6, p+10, p+12) are one of the two types of densest permissible constellations of 5 primes. Maximal gaps between quintuplets of this type are listed in A201062; see more comments there.

Links

Alexei Kourbatov, Table of n, a(n) for n = 1..71

Tony Forbes, Prime k-tuplets

G. H. Hardy and J. E. Littlewood, Some problems of 'Partitio numerorum'; III: on the expression of a number as a sum of primes, Acta Mathematica, Vol. 44, pp. 1-70, 1923.

Alexei Kourbatov, Maximal gaps between prime 5-tuples (graphs/data up to 10^15)

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 90 between quintuplets starting at p=7 and p=97 is the very first gap, so a(1)=7. The gap of 1770 between quintuplets starting at p=97 and p=1867 is a maximal gap - larger than any preceding gap; therefore a(2)=97. The gap after p=1867 is smaller, so a new term is not added.

Crossrefs

Cf. A022007 (prime 5-tuples p, p+4, p+6, p+10, p+12), A201062, A233433.

Sequence in context: A174315 A046908 A005014 * A333246 A335922 A157035

Adjacent sequences: A201060 A201061 A201062 * A201064 A201065 A201066

Keyword

nonn

Author

Alexei Kourbatov, Nov 26 2011

Status

approved