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 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 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 W. Weisstein, k-Tuple 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

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Last modified November 30 15:02 EST 2015. Contains 264669 sequences.