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 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 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
KEYWORD
nonn
AUTHOR
Alexei Kourbatov, Nov 26 2011
STATUS
approved