%I #37 Jul 03 2024 22:36:19
%S 1,1,3,4,6,8,10,12,15,17,20,23,25,28,32,35,38,41,45,49,52,56,60,64,68,
%T 72,76,81,85,89,94,98,103,108,113,117,122,127,132,138,143,148,153,159,
%U 164,170,175,181,187,192,198,204,210,216,222,228,234,240,247,253
%N Least integer j such that Sum_{i=1..j} 1/i^(1/3) >= n.
%H Sela Fried, <a href="/A054040/a054040_1.pdf">On the partial sums of the Zeta function Sum_{n>=1} 1/n^s for 0 < s < 1</a>, 2024.
%e a(7)=12 since Sum_{i=1..12} 1/i^(1/3) = 7.106248... and Sum_{i=1..11} 1/i^(1/3) = 6.669458... .
%t s = 0; i = 0; Table[i++; While[s = s + 1/(i^(1/3)); s < n, i++]; i, {n, 100}] (* _T. D. Noe_, Nov 09 2013 *)
%t Module[{nn=300,c},c=Accumulate[1/Surd[Range[nn],3]];Table[Position[ c,_?(#>=n&),1,1],{n,0,60}]]//Flatten (* _Harvey P. Dale_, Aug 14 2021 *)
%o (JavaScript)
%o s=0;n=1;
%o for (i=1;i<30;i++) {
%o s+=1/Math.pow(i,1/3);
%o if (s>=n) {n++;document.write(Math.floor(i)+", ");}
%o }
%Y Cf. A004080, A054040, A054041 (condition >n).
%Y Cf. A067086.
%K nonn
%O 0,3
%A _Carmine Suriano_, Nov 08 2013
%E a(0) added by _Jon Perry_, Nov 10 2013