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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. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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].
LINKS
EXAMPLE
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.
Sequence in context: A140565 A191072 A153418 * A191034 A340466 A222219
KEYWORD
fini,full,nonn
AUTHOR
Labos Elemer, Jan 24 2003
EXTENSIONS
Corrected by Rick L. Shepherd, Aug 30 2003
STATUS
approved

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Last modified September 23 19:57 EDT 2023. Contains 365554 sequences. (Running on oeis4.)