A073347 a(1)=1; a(n+1) is the smallest integer > a(n) such that Sum_{k=a(n)..a(n+1)} 1/sqrt(k) > Pi.

1, 5, 14, 28, 46, 69, 97, 130, 168, 211, 259, 311, 368, 430, 497, 569, 646, 728, 815, 907, 1004, 1105, 1211, 1322, 1438, 1559, 1685, 1816, 1952, 2093, 2239, 2390, 2546, 2706, 2871, 3041, 3216, 3396, 3581, 3771, 3966, 4166, 4371, 4581, 4796, 5016, 5240, 5469

Offset: 1

Author

Benoit Cloitre, Aug 23 2002

Keywords

• easy
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..600

Crossrefs

Cf. A091476.

Programs

Mathematica

a[1] = 1; a[n_] := a[n] = Module[{k = a[n - 1], s = 0}, While[(s += 1/Sqrt[k]) < Pi, k++]; k]; Array[a, 50] (* Amiram Eldar, May 19 2022 *)

Formula

a(n) is asymptotic to Pi^2*n^2/4.

Extensions

a(1) = 1 inserted by Amiram Eldar, May 19 2022