

A202362


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


2



9853497737, 22741837817, 242360943257, 1418575498577, 4396774576277, 8639103445097, 11105292314087, 12728490626207, 119057768524127, 226608256438997, 581653272077387, 896217252921227, 987041423819807, 1408999953009347, 1419018243046487, 2189095026865907
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


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.


LINKS

Dana Jacobsen, Table of n, a(n) for n = 1..27
T. Forbes, Prime ktuplets
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, 170, 1923.
Alexei Kourbatov, Maximal gaps between prime ktuples
Eric W. Weisstein, kTuple Conjecture


EXAMPLE

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.


PROG

(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


CROSSREFS

Cf. A027570 (prime decuplets p+0,2,6,12,14,20,24,26,30,32), A202361.
Sequence in context: A022251 A015385 A027570 * A204058 A154532 A157745
Adjacent sequences: A202359 A202360 A202361 * A202363 A202364 A202365


KEYWORD

nonn


AUTHOR

Alexei Kourbatov, Dec 18 2011


STATUS

approved



