A202282 Initial prime in prime decuplets (p+0,2,6,8,12,18,20,26,30,32) preceding the maximal gaps in A202281.

11, 33081664151, 83122625471, 294920291201, 730121110331, 1291458592421, 4700094892301, 6218504101541, 7908189600581, 10527733922591, 21939572224301, 23960929422161, 30491978649941, 46950720918371, 84254447788781, 118565337622001, 124788318636251, 235474768767851

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

Cf. A027569 (prime decuplets p+0,2,6,8,12,18,20,26,30,32), A202281, A202361, A202362.

Sequence in context: A247846 A257127 A027569 * A131680 A339268 A262595

Adjacent sequences: A202279 A202280 A202281 * A202283 A202284 A202285

Keyword

nonn

Author

Alexei Kourbatov, Dec 15 2011

Status

approved