A136269 Floor of sum of the first 10^n cube roots.

1, 16, 350, 7504, 161593, 3481214, 75000049, 1615826124, 34811916483, 750000000499, 16158260176316, 348119162523278, 7500000000004999, 161582601752402051, 3481191625209607376, 75000000000000049999, 1615826017523912899040, 34811916252095841925154

Offset

0,2

Comments

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

The conjecture is true (see links) - Sela Fried, Oct 02 2024.

Links

Table of n, a(n) for n=0..17.

Sela Fried, On the partial sums of Sum_{n=1..oo} n^s for 0 < s < 1.

Sela Fried, Proofs of some Conjectures from the OEIS, arXiv:2410.07237 [math.NT], 2024. See p. 3.

Example

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

Prog

(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)", "))

Crossrefs

Sequence in context: A227102 A221577 A363383 * A010368 A053103 A223032

Adjacent sequences: A136266 A136267 A136268 * A136270 A136271 A136272

Keyword

nonn

Author

Cino Hilliard, Mar 19 2008

Status

approved