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%I #6 Oct 15 2013 22:31:49
%S 3,11,17,23,41,47,59,83,89,107,131,137,179,191,251,293,317,347,353,
%T 359,389,401,467,503,521,593,599,653,887,947,971,1031,1151,1193,1229,
%U 1259,1301,1307,1439,1601,1931,1979,1997,2069,2531,3167,3299,4241,5261,5639,5849,8081,10091,17189,18041,19421
%N Suppose p and q = p+20 are primes. Define the difference pattern of (p,q) to be the successive differences of the primes in the range p to q. There are 56 possible difference patterns, shown in the Comments line. Sequence gives smallest value of p for each difference pattern, sorted by magnitude.
%C The 56 difference patterns are [20], [2,18], [6,14], [8,12], [12,8], [14,6], [18,2], [2,4,14], [2,6,12], [2,10,8], [2,12,6], [2,16,2], [6,2,12], [6,6,8], [6,8,6], [6,12,2], [8,4,8], [8,6,6], [8,10,2], [12,2,6], [12,6,2], [14,4,2], [2,4,2,12], [2,4,6,8], [2,4,8,6], [2,4,12,2], [2,6,4,8], [2,6,6,6], [2,6,10,2], [2,10,2,6], [2,10,6,2], [2,12,4,2], [6,2,4,8], [6,2,6,6], [6,2,10,2], [6,6,2,6], [6,6,6,2], [6,8,4,2], [8,4,2,6], [8,4,6,2], [8,6,4,2], [12,2,4,2], [2,4,2,4,8], [2,4,2,10,2], [2,4,6,2,6], [2,4,6,6,2], [2,6,4,2,6], [2,6,4,6,2], [2,6,6,4,2], [2,10,2,4,2], [6,2,4,6,2], [6,2,6,4,2], [8,4,2,4,2], [2,4,2,4,6,2], [2,6,4,2,4,2], [2,2,4,2,4,2,4].
%C Certain patterns are singular, i.e. occur only once like [2,2,4,2,4,2,4]. Impossible patterns are [2,14,4] or [10,10] etc.
%e p=10091, q=10111 has difference pattern [2, 6, 4, 8] and {10091, 10093, 10099, 10103, 10111} is the corresponding consecutive prime 5-tuple.
%Y A000230(10)=A031938(1)=887, A078951(1)=3299, A078965(1)=47, A078968(1)=251.
%Y Cf. A079016-A079024.
%K fini,full,nonn
%O 1,1
%A _Labos Elemer_, Jan 24 2003
%E Edited by _Rick L. Shepherd_, Sep 10 2003
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