A052381 The smallest initial prime of 2 non-overlapping d-twin primes if the distance between pairs (D) is minimal (see A052380).

3, 7, 47, 389, 409, 199, 24749, 3373, 20183, 46703, 19867, 16763, 142811, 14563, 69593, 763271, 276637, 255767, 363989, 383179, 247099, 2130809, 15370423, 3565931, 458069, 9401647, 6314393, 20823437, 9182389, 4911251, 15442121

Offset

1,1

Comments

A prime quadruple (triple), {[p,p+d],[p+D,p+D+d]} is called a "non-overlapping" (disjoint or touching) pair of twins if D = distance >= d = difference "inside" twin.

Links

Table of n, a(n) for n=1..31.

Formula

Smallest p so that [p, p+2n], [p+min{D}, p+2n+min{D}] is a quadruple (or triple if d=min{D}) of consecutive primes.

Example

If n=23, d=46, min{D}=48 then the first suitable quadruple of primes is [15370423, 15370469, 15370471, 15370517] with difference pattern [46, 2, 46]; if n=3, d=6, min{D}=6 then the first such triple is [47, 53, 53, 59] = [47, 53, 59] with difference pattern [6, 6].

Crossrefs

The first 10 terms here appear as initial terms in A052350-A052359.

See also A052380, A031924-A031928, A053318-A053331, A052350-A052359, A047948, A001223.

Sequence in context: A318087 A005650 A020754 * A219877 A031440 A331038

Adjacent sequences: A052378 A052379 A052380 * A052382 A052383 A052384

Keyword

nonn

Author

Labos Elemer, Mar 13 2000

Extensions

Corrected by Jud McCranie, Jan 04 2001

a(11) corrected by Sean A. Irvine, Nov 07 2021

Status

approved