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.

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

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