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%I #15 May 17 2016 12:05:28
%S 4,6,6,14,12,10,12,6,12,34,10,24,8,16,6,10,12,6,16,20,12,34,22,10,6,6,
%T 18,12,18,14,22,18,12,36,14,20,8,52,10,10,16,38,34,6,40,24,10,16,12,
%U 14,8,18,20,30,20,32,18,34,40,48,10,6,8,18,10,18,18,30,30,30,42,20,6,44
%N Least difference of primes p, q such that p < n^3 < q.
%C Least m such that a(m)=2*n for n=1,2,3,... are: {2,3,14,7,6,5,15,28,21,24,13,...}. - _Zak Seidov_, May 10 2016
%C There are numbers k other than 2 such that a(k) = 4. The first few (up to 1000) are 129 189 369 435 549 555 561 819. Conjecture: every even integer greater than 2 occurs infinitely often in this sequence. - _Franklin T. Adams-Watters_, May 13 2016
%H Zak Seidov, <a href="/A077038/b077038.txt">Table of n, a(n) for n = 2..10000</a>
%F a(n) = A014220(n) - A077037(n).
%t Table[c=n^3;NextPrime[c]-NextPrime[c,-1],{n,2,80}] (* _Harvey P. Dale_, Sep 14 2012 *)
%Y Cf. A058043, A000578.
%K nonn
%O 2,1
%A _Reinhard Zumkeller_, Oct 21 2002
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