OFFSET
1,1
COMMENTS
Prime decuplets (p+0,2,6,8,12,18,20,26,30,32) are one of the two types of densest permissible constellations of 10 primes. Maximal gaps between decuplets of this type are listed in A202281; see more comments there.
LINKS
Norman Luhn, Table of n, a(n) for n = 1..50 (terms 1..33 from Dana Jacobsen).
Tony Forbes and Norman Luhn, 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 Math. 44, 1-70, 1923.
Alexei Kourbatov, Maximal gaps between prime k-tuples
Eric Weisstein's World of Mathematics, k-Tuple Conjecture
EXAMPLE
The first four gaps (after the decuplets starting at p=11, 33081664151, 83122625471, 294920291201) form an increasing sequence, with the size of each gap setting a new record. Therefore these values of p are in the sequence, as a(1), a(2), a(3), a(4). The next gap is not a record, so the respective initial prime is not in the sequence.
PROG
(Perl) use ntheory ":all"; my($i, $l, $max)=(-1, 0, 0); for (sieve_prime_cluster(1, 1e13, 2, 6, 8, 12, 18, 20, 26, 30, 32)) { my $gap=$_-$l; if ($gap>$max) { say "$i $l" if ++$i > 0; $max=$gap; } $l=$_; } # Dana Jacobsen, Oct 09 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexei Kourbatov, Dec 15 2011
STATUS
approved