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

1,1

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.

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

Example

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.

Crossrefs

Cf. A022006 (prime 5-tuples p, p+2, p+6, p+8, p+12), A201073, A233432.

Sequence in context: A088268 A030085 A022006 * A056111 A090160 A062652

Adjacent sequences: A201071 A201072 A201073 * A201075 A201076 A201077

Keyword

nonn

Author

Alexei Kourbatov, Nov 26 2011

Status

approved