A202362 Initial prime in prime decuplets (p+0,2,6,12,14,20,24,26,30,32) preceding the maximal gaps in A202361.

9853497737, 22741837817, 242360943257, 1418575498577, 4396774576277, 8639103445097, 11105292314087, 12728490626207, 119057768524127, 226608256438997, 581653272077387, 896217252921227, 987041423819807, 1408999953009347, 1419018243046487, 2189095026865907

Offset: 1

Author

Alexei Kourbatov, Dec 18 2011

Keywords

• nonn

Comments

Prime decuplets (p+0,2,6,12,14,20,24,26,30,32) are one of the two types of densest permissible constellations of 10 primes. Maximal gaps between decuplets of this type are listed in A202361; see more comments there.

Examples

			The gap of 12102794130 between the very first decuplets starting at p=9853497737 and p=21956291867 means that the initial term is a(1)=9853497737.
The next gap after the decuplet starting at p=21956291867 is smaller, so it does not contribute to this sequence.
The next gap of 141702673770 between the decuplets at p=22741837817 and p=164444511587 is a new record; therefore the next term is a(2)=22741837817.
		

Links

• Norman Luhn, Table of n, a(n) for n = 1..44 (terms 1..27 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

Crossrefs

Cf. A027570 (prime decuplets p+0,2,6,12,14,20,24,26,30,32), A202281, A202282, A202361.

Programs

Perl

use ntheory ":all"; my($i,$l,$max)=(-1,0,0); for (sieve_prime_cluster(1,1e13,2,6,12,14,20,24,26,30,32)) { my $gap=$-$l; if ($gap>$max) { say "$i $l" if ++$i > 0; $max=$gap; } $l=$; } # Dana Jacobsen, Oct 09 2015