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A079021 Suppose p and q = p+22 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 51 possible difference patterns, shown in the Comments line. Sequence gives smallest value of p for each difference pattern, sorted by magnitude.

%I A079021 #4 Oct 15 2013 22:31:49
%S A079021 7,19,31,37,61,67,79,109,127,151,157,211,241,271,331,337,397,409,421,
%T A079021 457,487,499,541,619,661,739,751,787,919,991,1069,1129,1471,1531,1597,
%U A079021 1867,2221,2287,2671,2707,2797,2857,3187,3301,3391,3637,4651,6547,12637,17011,90001
%N A079021 Suppose p and q = p+22 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 51 possible difference patterns, shown in the Comments line. Sequence gives smallest value of p for each difference pattern, sorted by magnitude.
%C A079021 The 51 difference patterns are [22], [4,18], [6,16], [10,12], [12,10], [16,6], [18,4], [4,2,16], [4,6,12], [4,8,10], [4,12,6], [4,14,4], [6,4,12], [6,6,10], [6,10,6], [6,12,4], [10,2,10], [10,6,6], [10,8,4], [12,4,6], [12,6,4], [16,2,4], [4,2,4,12], [4,2,6,10], [4,2,10,6], [4,6,2,10], [4,6,6,6], [4,6,8,4], [4,8,4,6], [4,8,6,4], [6,4,2,10], [6,4,6,6], [6,4,8,4], [6,6,4,6], [6,6,6,4], [6,10,2,4], [10,2,4,6], [10,2,6,4], [10,6,2,4], [12,4,2,4], [4,2,4,2,10], [4,2,4,6,6], [4,2,6,4,6], [4,6,2,4,6], [4,6,2,6,4], [6,4,2,4,6], [6,4,2,6,4], [6,4,6,2,4], [6,6,4,2,4], [10,2,4,2,4], [4,2,4,2,4,6].
%C A079021 Certain patterns are singular, i.e. occur only once like [4,2,4,2,4,6].
%e A079021 p=6547, q=6569 has difference pattern [4,2,10,6] and {6547,6551,6553,6563,6569} is the corresponding consecutive prime 5-tuple.
%Y A079021 A078957(1)=12637, A078964(1)=157, A078967(1)=151, A078969(1)=3301, A000230(11)=1129. Cf. A079016-A079024.
%K A079021 fini,full,nonn
%O A079021 1,1
%A A079021 _Labos Elemer_, Jan 24 2003