A137262 Floor of sum of the first 10^n square roots.

1, 22, 671, 21097, 666716, 21082008, 666667166, 21081852648, 666666671666, 21081851083600, 666666666716666, 21081851067947309, 666666666667166666, 21081851067790776685, 666666666666671666666, 21081851067789211358047, 666666666666666716666666, 21081851067789195704773173

Offset

0,2

Links

Amiram Eldar, Table of n, a(n) for n = 0..666

Formula

From Amiram Eldar, Jul 18 2025: (Start)

a(n) = A025224(10^n).

a(n) ~ (2/3) * 10^(3*n/2). (End)

Example

The first 10^0 square roots is 1. The sum of the first 10^1 square roots is 22.468278186... . So 22 is the second entry in the sequence.

Mathematica

a[n_] := Floor[Sum[Sqrt[j], {j, 10^n}]]; Array[a, 17, 0] (* James C. McMahon, May 17 2025 *)
a[n_] := Floor[HarmonicNumber[10^n, -1/2]]; Array[a, 20, 0] (* Amiram Eldar, Jul 18 2025 *)

Prog

(PARI) g2(n, p=2) = for(j=0, n, s=0; for(x=0, 10^j, s+=x^(1/p)); print1(floor(s)", "))

Crossrefs

Cf. A025224, A195284.

Sequence in context: A218478 A223624 A230836 * A300137 A025760 A229124

Adjacent sequences: A137259 A137260 A137261 * A137263 A137264 A137265

Keyword

nonn

Author

Cino Hilliard, Mar 12 2008

Extensions

a(10)-a(16) from James C. McMahon, May 17 2025

a(17) from Amiram Eldar, Jul 18 2025

Status

approved