

A159910


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


2



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
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OFFSET

1,2


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


LINKS

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


FORMULA

a(n) = (A007530(n+1)A007530(n))/30 = A014561(n)A014561(n1) for n>1.


EXAMPLE

a(2) = A014561(2)A014561(1) = 30, a(3) = A014561(3)A014561(2) = 63, ...


PROG

(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((so)\30, ", "); ); (so)\30}


CROSSREFS

Cf. A007530, A014561, A047299.
Sequence in context: A112534 A006656 A205452 * A172485 A230647 A130723
Adjacent sequences: A159907 A159908 A159909 * A159911 A159912 A159913


KEYWORD

nonn


AUTHOR

M. F. Hasler, May 04 2009


STATUS

approved



