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A079020 Suppose p and q = p+20 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 56 possible difference patterns, shown in the Comments line. Sequence gives smallest value of p for each difference pattern, sorted by magnitude. 0
3, 11, 17, 23, 41, 47, 59, 83, 89, 107, 131, 137, 179, 191, 251, 293, 317, 347, 353, 359, 389, 401, 467, 503, 521, 593, 599, 653, 887, 947, 971, 1031, 1151, 1193, 1229, 1259, 1301, 1307, 1439, 1601, 1931, 1979, 1997, 2069, 2531, 3167, 3299, 4241, 5261, 5639, 5849, 8081, 10091, 17189, 18041, 19421 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The 56 difference patterns are [20], [2,18], [6,14], [8,12], [12,8], [14,6], [18,2], [2,4,14], [2,6,12], [2,10,8], [2,12,6], [2,16,2], [6,2,12], [6,6,8], [6,8,6], [6,12,2], [8,4,8], [8,6,6], [8,10,2], [12,2,6], [12,6,2], [14,4,2], [2,4,2,12], [2,4,6,8], [2,4,8,6], [2,4,12,2], [2,6,4,8], [2,6,6,6], [2,6,10,2], [2,10,2,6], [2,10,6,2], [2,12,4,2], [6,2,4,8], [6,2,6,6], [6,2,10,2], [6,6,2,6], [6,6,6,2], [6,8,4,2], [8,4,2,6], [8,4,6,2], [8,6,4,2], [12,2,4,2], [2,4,2,4,8], [2,4,2,10,2], [2,4,6,2,6], [2,4,6,6,2], [2,6,4,2,6], [2,6,4,6,2], [2,6,6,4,2], [2,10,2,4,2], [6,2,4,6,2], [6,2,6,4,2], [8,4,2,4,2], [2,4,2,4,6,2], [2,6,4,2,4,2], [2,2,4,2,4,2,4].

Certain patterns are singular, i.e. occur only once like [2,2,4,2,4,2,4]. Impossible patterns are [2,14,4] or [10,10] etc.

LINKS

Table of n, a(n) for n=1..56.

EXAMPLE

p=10091, q=10111 has difference pattern [2, 6, 4, 8] and {10091, 10093, 10099, 10103, 10111} is the corresponding consecutive prime 5-tuple.

CROSSREFS

A000230(10)=A031938(1)=887, A078951(1)=3299, A078965(1)=47, A078968(1)=251.

Cf. A079016-A079024.

Sequence in context: A019397 A108328 A153419 * A118590 A136082 A106083

Adjacent sequences:  A079017 A079018 A079019 * A079021 A079022 A079023

KEYWORD

fini,full,nonn

AUTHOR

Labos Elemer, Jan 24 2003

EXTENSIONS

Edited by Rick L. Shepherd, Sep 10 2003

STATUS

approved

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Last modified November 22 08:46 EST 2019. Contains 329389 sequences. (Running on oeis4.)