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A292775 a(n) = smallest prime q such that Sum_{primes p <= q} 1/sqrt(p) >= n.

%I A292775 #24 Oct 13 2017 12:43:27
%S A292775 3,7,19,41,73,113,191,271,383,509,661,859,1069,1307,1601,1931,2287,
%T A292775 2687,3119,3583,4093,4657,5279,5881,6607,7351,8167,9001,9851,10837,
%U A292775 11867,12899,13967,15161,16361,17627,19031,20389,21821,23297,24917,26557,28279,30059,31891,33647,35617,37607,39779
%N A292775 a(n) = smallest prime q such that Sum_{primes p <= q} 1/sqrt(p) >= n.
%H A292775 Vincenzo Librandi, <a href="/A292775/b292775.txt">Table of n, a(n) for n = 1..500</a>
%H A292775 Benoit Cloitre, <a href="/A292775/a292775.pdf">Asymptotics for A292775</a>
%F A292775 a(n) ~ prime(n)^2. - _Benoit Cloitre_, Oct 01 2017 [See link]
%p A292775 Digits:=50;
%p A292775 s0:=0; k:=1; lisi:=[]; lisP:=[];
%p A292775 for i from 1 to 10000 do p:=ithprime(i);
%p A292775 s0:=s0+evalf(1/sqrt(p));
%p A292775 if s0 >= k then k:=k+1; lisi:=[op(lisi),i]; lisP:=[op(lisP),p]; fi;
%p A292775 od:
%p A292775 lisi; # A292774
%p A292775 lisP; # A292775
%t A292775 f[n_]:=Block[{k=0, s=0}, While[s<n, k++; s=N[s+1/Sqrt[Prime[k]], 50]]; k]; Table[Prime[f[n]], {n, 1, 50}] (* _Vincenzo Librandi_, Oct 01 2017 *)
%Y A292775 Cf. A292774; A019529, A054040.
%K A292775 nonn
%O A292775 1,1
%A A292775 _N. J. A. Sloane_, Sep 30 2017