A078964 -id:A078964 - cp's OEIS frontend

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.

7, 19, 31, 37, 61, 67, 79, 109, 127, 151, 157, 211, 241, 271, 331, 337, 397, 409, 421, 457, 487, 499, 541, 619, 661, 739, 751, 787, 919, 991, 1069, 1129, 1471, 1531, 1597, 1867, 2221, 2287, 2671, 2707, 2797, 2857, 3187, 3301, 3391, 3637, 4651, 6547, 12637, 17011, 90001

Offset: 1

Labos Elemer, Jan 24 2003

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].

Certain patterns are singular, i.e. occur only once like [4,2,4,2,4,6].

			p=6547, q=6569 has difference pattern [4,2,10,6] and {6547,6551,6553,6563,6569} is the corresponding consecutive prime 5-tuple.

A078957(1)=12637, A078964(1)=157, A078967(1)=151, A078969(1)=3301, A000230(11)=1129. Cf. A079016-A079024.

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