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

Author

Alexei Kourbatov, Nov 26 2011

Keywords

• nonn

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.

Examples

			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.
		

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

Crossrefs

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