A136269 - OEIS

%I #14 Oct 14 2024 11:24:38

%S 1,16,350,7504,161593,3481214,75000049,1615826124,34811916483,

%T 750000000499,16158260176316,348119162523278,7500000000004999,

%U 161582601752402051,3481191625209607376,75000000000000049999,1615826017523912899040,34811916252095841925154

%N Floor of sum of the first 10^n cube roots.

%C Conjecture: For n = 3k, a(n) = (3/4)*10^(4n/3)+5*10^(n/3-1)-1.

%C The conjecture is true (see links) - _Sela Fried_, Oct 02 2024.

%H Sela Fried, <a href="/A136269/a136269.pdf">On the partial sums of Sum_{n=1..oo} n^s for 0 < s < 1</a>.

%H Sela Fried, <a href="https://arxiv.org/abs/2410.07237">Proofs of some Conjectures from the OEIS</a>, arXiv:2410.07237 [math.NT], 2024. See p. 3.

%e For n = 6, a(6) = (3/4)*10^8 + 5* 10^1-1 = 75000049.

%o (PARI) /* For this sequence, p = 3 */ g2(n,p) = for(j=0,n,s=0;for(x=0,10^j,s+=x^(1/p));print1(floor(s)","))

%K nonn

%O 0,2

%A _Cino Hilliard_, Mar 19 2008