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

3, 7, 19, 41, 73, 113, 191, 271, 383, 509, 661, 859, 1069, 1307, 1601, 1931, 2287, 2687, 3119, 3583, 4093, 4657, 5279, 5881, 6607, 7351, 8167, 9001, 9851, 10837, 11867, 12899, 13967, 15161, 16361, 17627, 19031, 20389, 21821, 23297, 24917, 26557, 28279, 30059, 31891, 33647, 35617, 37607, 39779

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..500

Benoit Cloitre, Asymptotics for A292775

Formula

a(n) ~ prime(n)^2. - Benoit Cloitre, Oct 01 2017 [See link]

Maple

Digits:=50;
s0:=0; k:=1; lisi:=[]; lisP:=[];
for i from 1 to 10000 do p:=ithprime(i);
s0:=s0+evalf(1/sqrt(p));
if s0 >= k then k:=k+1; lisi:=[op(lisi), i]; lisP:=[op(lisP), p]; fi;
od:
lisi; # A292774
lisP; # A292775

Mathematica

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 *)

Crossrefs

Cf. A292774; A019529, A054040.

Sequence in context: A281866 A173114 A163572 * A282024 A356617 A086519

Adjacent sequences: A292772 A292773 A292774 * A292776 A292777 A292778

Keyword

nonn

Author

N. J. A. Sloane, Sep 30 2017

Status

approved