A201074 Initial primes in prime 5-tuples (p, p+2, p+6, p+8, p+12) preceding the maximal gaps in A201073.

5, 11, 101, 1481, 22271, 55331, 536441, 661091, 1461401, 1615841, 5527001, 11086841, 35240321, 53266391, 72610121, 92202821, 117458981, 196091171, 636118781, 975348161, 1156096301, 1277816921, 1347962381, 2195593481, 3128295551

Offset: 1

Author

Alexei Kourbatov, Nov 26 2011

Keywords

• nonn

Comments

Prime quintuplets (p, p+2, p+6, p+8, 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 A201073; see more comments there.

Examples

			The initial four gaps of 6, 90, 1380, 14580 (starting at p=5, 11, 101, 1481) form an increasing sequence of records. Therefore a(1)=5, a(2)=11, a(3)=101, and a(4)=1481. The next gap is smaller, so a new term is not added.
		

Links

• Alexei Kourbatov, Table of n, a(n) for n = 1..64
• 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. A022006 (prime 5-tuples p, p+2, p+6, p+8, p+12), A201073, A233432.