cp's OEIS Frontend

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

%I A159910 #16 Jul 05 2020 13:42:10
%S A159910 0,3,3,21,22,13,7,39,7,73,126,119,88,3,11,66,29,17,53,42,101,214,104,
%T A159910 298,252,133,255,141,76,91,168,81,45,56,203,301,43,66,291,223,92,97,
%U A159910 442,290,437,281,38,144,549,241,29,192,11,518,266,490,122,130,13,329,85,209
%N A159910 Distance of prime quadruplets divided by 30, rounded towards the nearest integer.
%C A159910 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.
%C A159910 All terms are of the form {0, 1, 3, 4, 6} mod 7. - _Hugo Pfoertner_, May 29 2020
%H A159910 Hugo Pfoertner, <a href="/A159910/b159910.txt">Table of n, a(n) for n = 1..10000</a>
%F A159910 a(n) = (A007530(n+1)-A007530(n))/30 = A014561(n)-A014561(n-1) for n>1.
%e A159910 a(2) = A014561(2)-A014561(1) = 3-0, a(3) = A014561(3)-A014561(2) = 6-3, ...
%o A159910 (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}
%Y A159910 Cf. A007530, A014561, A047299.
%K A159910 nonn
%O A159910 1,2
%A A159910 _M. F. Hasler_, May 04 2009