This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A137262 #22 Jul 18 2025 04:26:16
%S A137262 1,22,671,21097,666716,21082008,666667166,21081852648,666666671666,
%T A137262 21081851083600,666666666716666,21081851067947309,666666666667166666,
%U A137262 21081851067790776685,666666666666671666666,21081851067789211358047,666666666666666716666666,21081851067789195704773173
%N A137262 Floor of sum of the first 10^n square roots.
%H A137262 Amiram Eldar, <a href="/A137262/b137262.txt">Table of n, a(n) for n = 0..666</a>
%F A137262 From _Amiram Eldar_, Jul 18 2025: (Start)
%F A137262 a(n) = A025224(10^n).
%F A137262 a(n) ~ (2/3) * 10^(3*n/2). (End)
%e A137262 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.
%t A137262 a[n_] := Floor[Sum[Sqrt[j],{j,10^n}]];Array[a,17,0] (* _James C. McMahon_, May 17 2025 *)
%t A137262 a[n_] := Floor[HarmonicNumber[10^n, -1/2]]; Array[a, 20, 0] (* _Amiram Eldar_, Jul 18 2025 *)
%o A137262 (PARI) g2(n,p=2) = for(j=0,n,s=0;for(x=0,10^j,s+=x^(1/p)); print1(floor(s)", "))
%Y A137262 Cf. A025224, A195284.
%K A137262 nonn
%O A137262 0,2
%A A137262 _Cino Hilliard_, Mar 12 2008
%E A137262 a(10)-a(16) from _James C. McMahon_, May 17 2025
%E A137262 a(17) from _Amiram Eldar_, Jul 18 2025