A079019 Suppose p and q = p+18 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 49 possible difference patterns, shown in the Comments line. Sequence gives smallest value of p for each difference pattern, sorted by magnitude.

5, 11, 13, 19, 23, 29, 41, 43, 61, 71, 79, 83, 89, 109, 113, 131, 139, 149, 179, 181, 193, 211, 239, 251, 331, 401, 461, 491, 503, 523, 569, 601, 659, 691, 733, 739, 743, 821, 1303, 1531, 1601, 1861, 1931, 1933, 1993, 2069, 3313, 4201, 18043

Offset: 1

Author

Labos Elemer, Jan 24 2003

Keywords

• fini
• full
• nonn

Comments

Difference patterns are [18], [2,16], [4,14], [6,12], [8,10], [10,8], [12,6], [14,4], [16,2], [2,4,12], [2,6,10], [2,10,6], [2,12,4], [4,2,12], [4,6,8], [4,8,6], [4,12,2], [6,2,10], [6,4,8], [6,6,6], [6,8,4], [6,10,2], [8,4,6], [8,6,4], [10,2,6], [10,6,2], [12,2,4], [12,4,2], [2,4,2,10], [2,4,6,6], [2,6,4,6], [2,6,6,4], [2,10,2,4], [4,2,4,8], [4,2,10,2], [4,6,2,6], [4,6,6,2], [6,2,4,6], [6,2,6,4], [6,4,2,6], [6,4,6,2], [6,6,4,2], [8,4,2,4], [10,2,4,2], [2,4,2,4,6], [2,6,4,2,4], [4,2,4,6,2], [6,4,2,4,2], [2,4,2,4,2,4].

Examples

			p=18043, q=18061 has difference pattern [4,2,10,2] and {18043,18047,18049,18059,18061} is the corresponding consecutive prime 5-tuple.
		

Crossrefs

A078947[1]=41, A078949[1]=71, A078950[1]=149, A078955[1]=19, A078956[1]=43, A078959[1]=23, A078962[1]=61, A078966[1]=601, A078958[1]=1601, A078963[1]=3313, A031936[1]=A000230[9]=523.

Cf. A079016-A079024.

Extensions

Corrected by Rick L. Shepherd, Aug 30 2003