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