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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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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].

LINKS

Table of n, a(n) for n=1..51.

EXAMPLE

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

CROSSREFS

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

Sequence in context: A274971 A040045 A242476 * A216133 A079740 A030549

Adjacent sequences:  A079018 A079019 A079020 * A079022 A079023 A079024

KEYWORD

fini,full,nonn

AUTHOR

Labos Elemer, Jan 24 2003

STATUS

approved

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Last modified September 22 08:15 EDT 2021. Contains 347605 sequences. (Running on oeis4.)