This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A079063 #8 Feb 16 2025 08:32:48 %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, %T A079063 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 A079063 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 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="https://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) %K A079063 nonn %O A079063 1,1 %A A079063 _Benoit Cloitre_, Feb 02 2003