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%I #7 Mar 30 2012 18:39:12
%S 3,3,2,3,3,3,3,2,3,3,4,4,4,3,4,4,5,4,5,4,4,4,4,5,6,5,4,4,3,3,5,5,5,5,
%T 6,5,6,5,6,7,6,5,5,4,4,4,7,7,7,6,6,6,6,8,7,7,6,5,6,6,6,5,6,6,6,6,7,7,
%U 8,7,7,7,7,7,6,7,6,7,7,8,8,9,9,8,8,7,8,8,8,7,7,8,7,6,6,6,5,6,6,8,8,9,9,10
%N Least k such that sqrt(prime(n+k))-sqrt(prime(n))>1.
%C Inspired by Andrica's conjecture. If it is true, a(n)>1 for all n.
%C Cf. A038458, A074976, A078693
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AndricasConjecture.html">Andrica's conjecture</a>
%F Conjecture: there is a constant c>0 such that for n large enough, a(n)>c*sqrt(n) and we can take c=0.4. More precisely, there are 2 constants A and B such that A=lim sup n ->infinity a(n)/sqrt(n) exists = 0.75....; B=lim inf n ->infinity a(n)/sqrt(n) exists =0.46....
%o (PARI) a(n)=if(n<0,0,k=1; while(abs(sqrt(prime(n+k))-sqrt(prime(n)))<1,k++); k)
%K nonn
%O 1,1
%A _Benoit Cloitre_, Feb 02 2003
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