A202282 - OEIS

%I #26 Sep 15 2021 21:35:49

%S 11,33081664151,83122625471,294920291201,730121110331,1291458592421,

%T 4700094892301,6218504101541,7908189600581,10527733922591,

%U 21939572224301,23960929422161,30491978649941,46950720918371,84254447788781,118565337622001,124788318636251,235474768767851

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

%C 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.

%H Norman Luhn, <a href="/A202282/b202282.txt">Table of n, a(n) for n = 1..50</a> (terms 1..33 from Dana Jacobsen).

%H Tony Forbes and Norman Luhn, <a href="http://www.pzktupel.de/ktuplets.htm">Prime k-tuplets</a>

%H G. H. Hardy and J. E. Littlewood, <a href="http://dx.doi.org/10.1007/BF02403921">Some Problems of 'Partitio Numerorum.' III. On the Expression of a Number as a Sum of Primes</a>, Acta Math. 44, 1-70, 1923.

%H Alexei Kourbatov, <a href="http://www.javascripter.net/math/primes/maximalgapsbetweenktuples.htm">Maximal gaps between prime k-tuples</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/k-TupleConjecture.html">k-Tuple Conjecture</a>

%e 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.

%o (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

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

%K nonn

%O 1,1

%A _Alexei Kourbatov_, Dec 15 2011