%I A008407
%S A008407 2,6,8,12,16,20,26,30,32,36,42,48,50,56,60,66,70,76,80,84,90,94,100,
%T A008407 110,114,120,126,130,136,140,146,152,156,158,162,168,176,182,186,
%U A008407 188,196,200,210,212,216,226,236,240,246,252,254,264,270,272,278
%N A008407 Minimal difference s(n) between beginning and end of n consecutive large 
               primes (n-tuplet) permitted by divisibility considerations.
%C A008407 Tony Forbes defines a prime k-tuplet (distinguished from a prime k-tuple) 
               to be a maximally possible dense cluster of primes (a prime constellation) 
               which will necessarily involve consecutive primes whereas a prime 
               k-tuple is a prime cluster which may not necessarily be of maximum 
               possible density (in which case the primes are not necessarily consecutive.)
%C A008407 a(1) would be 0 (for a prime 1-tuplet.)
%D A008407 R. K. Guy, "Unsolved Problems in Number Theory", lists a number of relevant 
               papers in Section A8.
%D A008407 G. H. Hardy and J.E. Littlewood, "Partitio Numerorum III", Acta Math. 
               44 (1922) 1-70, see final section.
%D A008407 John Leech, "Groups of primes having maximum density", Math. Tables Aids 
               to Comput., 12 (1958) 144-145.
%H A008407 T. D. Noe, <a href="b008407.txt">Table of n, a(n) for n=2..672</a> (from 
               Engelsma's data)
%H A008407 Thomas J. Engelsma, <a href="http://www.opertech.com/primes/k-tuples.html">
               Permissible Patterns</a>
%H A008407 Tony Forbes, <a href="http://anthony.d.forbes.googlepages.com/ktuplets.htm"> 
               k-tuplets</a>
%H A008407 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PrimeConstellation.html">Prime Constellation.</a>
%F A008407 s(k), k >= 2, is smallest s such that there exist B = {b_1, b_2, ..., 
               b_k} with s = b_k - b_1 and such that for all primes p <= k, not 
               all residues modulo p are represented by B.
%Y A008407 Equals A020497 - 1.
%Y A008407 Sequence in context: A084724 A111051 A077561 this_sequence A111224 A139718 
               A135311
%Y A008407 Adjacent sequences: A008404 A008405 A008406 this_sequence A008408 A008409 
               A008410
%K A008407 nonn,nice
%O A008407 2,1
%A A008407 T. Forbes (anthony.d.forbes(AT)googlemail.com)
%E A008407 Correction from weidhaas(AT)wotan.llnl.gov (Pat Weidhaas) Jun 15 1997.
%E A008407 Edited by Daniel Forgues (squid(AT)zensearch.com), Aug 13 2009