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 A292774 #24 Oct 13 2017 12:45:11 %S A292774 2,4,8,13,21,30,43,58,76,97,121,149,180,214,252,294,340,390,444,502, %T A292774 564,630,700,775,854,937,1025,1118,1215,1317,1423,1535,1650,1771,1897, %U A292774 2027,2162,2303,2448,2598,2753,2914,3079,3250,3426,3607,3793,3984,4181,4383,4591,4803,5022,5245,5474,5709 %N A292774 a(n) = smallest m such that Sum_{i=1..m} 1/sqrt(prime(i)) >= n. %H A292774 Vincenzo Librandi, <a href="/A292774/b292774.txt">Table of n, a(n) for n = 1..500</a> %F A292774 a(n) ~ (n^2*log(n))/2. - _Benoit Cloitre_, Oct 01 2017 [This follows from the asymptotics for A292775] %p A292774 Digits:=50; %p A292774 s0:=0; k:=1; lisi:=[]; lisP:=[]; %p A292774 for i from 1 to 10000 do p:=ithprime(i); %p A292774 s0:=s0+evalf(1/sqrt(p)); %p A292774 if s0 >= k then k:=k+1; lisi:=[op(lisi),i]; lisP:=[op(lisP),p]; fi; %p A292774 od: %p A292774 lisi; # A292774 %p A292774 lisP; # A292775 %t A292774 f[n_]:=Block[{k=0, s=0}, While[s<n, k++; s=N[s+1/Sqrt[Prime[k]], 50]]; k]; Table[f[n], {n, 1, 60}] (* _Vincenzo Librandi_, Oct 01 2017 *) %Y A292774 Cf. A292775; A019529, A054040. %K A292774 nonn %O A292774 1,1 %A A292774 _N. J. A. Sloane_, Sep 30 2017