A159910 Distance of prime quadruplets divided by 30, rounded towards the nearest integer.

0, 3, 3, 21, 22, 13, 7, 39, 7, 73, 126, 119, 88, 3, 11, 66, 29, 17, 53, 42, 101, 214, 104, 298, 252, 133, 255, 141, 76, 91, 168, 81, 45, 56, 203, 301, 43, 66, 291, 223, 92, 97, 442, 290, 437, 281, 38, 144, 549, 241, 29, 192, 11, 518, 266, 490, 122, 130, 13, 329, 85, 209

Offset: 1

Author

M. F. Hasler, May 04 2009

Keywords

• nonn

Comments

First differences of A007530, divided by 30 (and rounded to 0 for a(1)). The first prime quadruplet is the only one not starting at 11 (mod 30), and has no corresponding value in A014561. The "distance" can mean distance of starting points, or distance of barycenters, but also the distance in the strict sense (differing by 8 from the former), which gives the same value after rounding to the nearest integer.

All terms are of the form {0, 1, 3, 4, 6} mod 7. - Hugo Pfoertner, May 29 2020

Examples

			a(2) = A014561(2)-A014561(1) = 3-0, a(3) = A014561(3)-A014561(2) = 6-3, ...
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007530, A014561, A047299.

Programs

PARI

A159910( n, list=0, s=5 )={ my(o,p,q,r); until(n--<0, o=s; until( p+8==s=nextprime(s+2), p=q; q=r; r=s); list & p>o & print1((s-o)\30,","););(s-o)\30}

Formula

a(n) = (A007530(n+1)-A007530(n))/30 = A014561(n)-A014561(n-1) for n>1.