cp's OEIS Frontend

A231405 Least integer j such that Sum_{i=1..j} 1/i^(1/3) >= n.

%I A231405 #37 Jul 03 2024 22:36:19
%S A231405 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 A231405 72,76,81,85,89,94,98,103,108,113,117,122,127,132,138,143,148,153,159,
%U A231405 164,170,175,181,187,192,198,204,210,216,222,228,234,240,247,253
%N A231405 Least integer j such that Sum_{i=1..j} 1/i^(1/3) >= n.
%H A231405 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 A231405 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 A231405 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 A231405 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 A231405 (JavaScript)
%o A231405 s=0;n=1;
%o A231405 for (i=1;i<30;i++) {
%o A231405 s+=1/Math.pow(i,1/3);
%o A231405 if (s>=n) {n++;document.write(Math.floor(i)+", ");}
%o A231405 }
%Y A231405 Cf. A004080, A054040, A054041 (condition >n).
%Y A231405 Cf. A067086.
%K A231405 nonn
%O A231405 0,3
%A A231405 _Carmine Suriano_, Nov 08 2013
%E A231405 a(0) added by _Jon Perry_, Nov 10 2013