A292774 a(n) = smallest m such that Sum_{i=1..m} 1/sqrt(prime(i)) >= n.

2, 4, 8, 13, 21, 30, 43, 58, 76, 97, 121, 149, 180, 214, 252, 294, 340, 390, 444, 502, 564, 630, 700, 775, 854, 937, 1025, 1118, 1215, 1317, 1423, 1535, 1650, 1771, 1897, 2027, 2162, 2303, 2448, 2598, 2753, 2914, 3079, 3250, 3426, 3607, 3793, 3984, 4181, 4383, 4591, 4803, 5022, 5245, 5474, 5709

Offset

1,1

Links

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

Formula

a(n) ~ (n^2*log(n))/2. - Benoit Cloitre, Oct 01 2017 [This follows from the asymptotics for A292775]

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[f[n], {n, 1, 60}] (* Vincenzo Librandi, Oct 01 2017 *)

Crossrefs

Cf. A292775; A019529, A054040.

Sequence in context: A115266 A164508 A308094 * A026039 A004978 A005282

Adjacent sequences: A292771 A292772 A292773 * A292775 A292776 A292777

Keyword

nonn

Author

N. J. A. Sloane, Sep 30 2017

Status

approved