A181354 Number of n-digit perfect cubes.

2, 2, 5, 12, 25, 53, 116, 249, 535, 1155, 2487, 5358, 11545, 24871, 53584, 115444, 248715, 535841, 1154435, 2487154, 5358411, 11544347, 24871542, 53584111, 115443470, 248715414, 535841116, 1154434691, 2487154143, 5358411166

Offset

1,1

Comments

a(n) is also the total number of n-digit numbers requiring 1 positive cube in their representation as sum of cubes.

a(n) + A181376(n) + A181378(n) + A181380(n) + A181384(n) + A181401(n) + A181403(n) + A181405(n) + A171386(n) = A052268(n).

Differs from A062941 only at n=1, because 0 is considered a 0-digit, not a 1-digit number here. - R. J. Mathar, Jul 09 2011

Links

Table of n, a(n) for n=1..30.

Eric Weisstein's World of Mathematics, Waring's Problem.

Formula

a(n) = A061439(n) - A061439(n-1).

Maple

a:=n->ceil(10^(n/3))-ceil(10^((n-1)/3));

Mathematica

With[{c = Range[4650000]^3}, Length[#]&/@Table[Select[c, IntegerLength[#] == n &], {n, 20}]] (* Harvey P. Dale, Feb 01 2011 *)
Differences[Ceiling[10^(Range[0, 30]/3)]]

Crossrefs

Cf. A000578

Sequence in context: A248664 A143195 A192799 * A085289 A095339 A216025

Adjacent sequences: A181351 A181352 A181353 * A181355 A181356 A181357

Keyword

nonn,base

Author

Martin Renner, Jan 28 2011

Extensions

More terms from T. D. Noe, Feb 01 2011

Status

approved