

A201074


Initial primes in prime quintuplets (p, p+2, p+6, p+8, p+12) preceding the maximal gaps in A201073.


3



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
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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 ktuplets
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. 170, 1923.
Alexei Kourbatov, Maximal gaps between prime quintuplets (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, kTuple 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 quintuplets 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



