A292775 - OEIS

%I #24 Oct 13 2017 12:43:27

%S 3,7,19,41,73,113,191,271,383,509,661,859,1069,1307,1601,1931,2287,

%T 2687,3119,3583,4093,4657,5279,5881,6607,7351,8167,9001,9851,10837,

%U 11867,12899,13967,15161,16361,17627,19031,20389,21821,23297,24917,26557,28279,30059,31891,33647,35617,37607,39779

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

%H Vincenzo Librandi, <a href="/A292775/b292775.txt">Table of n, a(n) for n = 1..500</a>

%H Benoit Cloitre, <a href="/A292775/a292775.pdf">Asymptotics for A292775</a>

%F a(n) ~ prime(n)^2. - _Benoit Cloitre_, Oct 01 2017 [See link]

%p Digits:=50;

%p s0:=0; k:=1; lisi:=[]; lisP:=[];

%p for i from 1 to 10000 do p:=ithprime(i);

%p s0:=s0+evalf(1/sqrt(p));

%p if s0 >= k then k:=k+1; lisi:=[op(lisi),i]; lisP:=[op(lisP),p]; fi;

%p od:

%p lisi; # A292774

%p lisP; # A292775

%t 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 Cf. A292774; A019529, A054040.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Sep 30 2017