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A201063 Initial primes in prime quintuplets (p, p+4, p+6, p+10, p+12) preceding the maximal gaps in A201062. 3
7, 97, 3457, 5647, 19417, 43777, 101107, 1621717, 3690517, 5425747, 8799607, 9511417, 16388917, 22678417, 31875577, 37162117, 64210117, 119732017, 200271517, 203169007, 241307107, 342235627, 367358347, 378200227 (list; graph; refs; listen; history; text; internal format)
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 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, 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 quintuplets p, p+4, p+6, p+10, p+12), A201062, A233433.

Sequence in context: A174315 A046908 A005014 * A157035 A022008 A200504

Adjacent sequences:  A201060 A201061 A201062 * A201064 A201065 A201066

KEYWORD

nonn

AUTHOR

Alexei Kourbatov, Nov 26 2011

STATUS

approved

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Last modified November 13 15:41 EST 2019. Contains 329106 sequences. (Running on oeis4.)