%I A079063
%S A079063 3,3,2,3,3,3,3,2,3,3,4,4,4,3,4,4,5,4,5,4,4,4,4,5,6,5,4,4,3,3,5,5,5,5,6,
%T A079063 5,6,5,6,7,6,5,5,4,4,4,7,7,7,6,6,6,6,8,7,7,6,5,6,6,6,5,6,6,6,6,7,7,8,7,
%U A079063 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 A079063 Least k such that sqrt(prime(n+k))-sqrt(prime(n))>1.
%C A079063 Inspired by Andrica's conjecture. If it is true, a(n)>1 for all n.
%C A079063 Cf. A038458, A074976, A078693
%H A079063 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               AndricasConjecture.html">Andrica's conjecture</a>
%F A079063 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 A079063 (PARI) a(n)=if(n<0,0,k=1; while(abs(sqrt(prime(n+k))-sqrt(prime(n)))<1,
               k++); k)
%Y A079063 Sequence in context: A060586 A076662 A164359 this_sequence A031352 A057853 
               A129309
%Y A079063 Adjacent sequences: A079060 A079061 A079062 this_sequence A079064 A079065 
               A079066
%K A079063 nonn
%O A079063 1,1
%A A079063 Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 02 2003