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

Author

Labos Elemer, Mar 13 2000

Keywords

• nonn

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.

Examples

			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.

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.

Extensions

Corrected by Jud McCranie, Jan 04 2001

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