This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A202362 #24 Feb 16 2025 08:33:16
%S A202362 9853497737,22741837817,242360943257,1418575498577,4396774576277,
%T A202362 8639103445097,11105292314087,12728490626207,119057768524127,
%U A202362 226608256438997,581653272077387,896217252921227,987041423819807,1408999953009347,1419018243046487,2189095026865907
%N A202362 Initial prime in prime decuplets (p+0,2,6,12,14,20,24,26,30,32) preceding the maximal gaps in A202361.
%C A202362 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.
%H A202362 Norman Luhn, <a href="/A202362/b202362.txt">Table of n, a(n) for n = 1..44</a> (terms 1..27 from Dana Jacobsen).
%H A202362 Tony Forbes and Norman Luhn, <a href="http://www.pzktupel.de/ktuplets.htm">Prime k-tuplets</a>
%H A202362 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 A202362 Alexei Kourbatov, <a href="http://www.javascripter.net/math/primes/maximalgapsbetweenktuples.htm">Maximal gaps between prime k-tuples</a>
%H A202362 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/k-TupleConjecture.html">k-Tuple Conjecture</a>
%e A202362 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.
%e A202362 The next gap after the decuplet starting at p=21956291867 is smaller, so it does not contribute to this sequence.
%e A202362 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.
%o A202362 (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
%Y A202362 Cf. A027570 (prime decuplets p+0,2,6,12,14,20,24,26,30,32), A202281, A202282, A202361.
%K A202362 nonn
%O A202362 1,1
%A A202362 _Alexei Kourbatov_, Dec 18 2011