A000433 n written in base where place values are positive cubes.

0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 100, 101, 102, 103, 104, 105, 106, 107, 110, 111, 112, 113, 114, 115, 116, 117, 120, 121, 122, 123, 124, 125, 126, 127, 130, 131, 132, 200, 201, 202, 203

Offset: 0

Author

R. Muller

Keywords

• nonn
• base
• easy
• look

Comments

Let [d1, d2, d3, ...] be the decimal expansion of the n-th term, then dk is the number of times that the greedy algorithm subtracts the cube k^3 with input n. - Joerg Arndt, Nov 21 2014

For n > 1: A048766(n) = number of digits of a(n); A190311(n) = number of nonzero digits of a(n); A055401(n) = sum of digits of a(n). - Reinhard Zumkeller, May 08 2011

First differs from numbers written in base 8 (A007094) at a(27) = 100, whereas A007094(27) = 33. - Alonso del Arte, Nov 27 2014

The rightmost (least significant) digit never exceeds 7, the second digit from the right never exceeds 3, the third digit never exceeds 2, and the rest are just 0's and 1's. - Ivan Neretin, Sep 03 2015

Examples

			a(26) = 32 because 26 = 3 * 2^3 + 2 * 1^3.
a(27) = 100 because 27 = 3^3 + 0 * 2^3 + 0 * 1^3.
a(28) = 101 because 28 = 3^3 + 0 * 2^3 + 1 * 1^3.
		

References

• Florentin Smarandache, "Properties of the Numbers", University of Craiova Archives, 1975; Arizona State University Special Collections, Tempe, AZ.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000578, A007961.

Programs

Haskell

import Data.Char (intToDigit)
a000433 0 = 0
a000433 n = read $ map intToDigit $
  t n $ reverse $ takeWhile (<= n) $ tail a000578_list where
      t _ []          = []
      t m (x:xs)
          | x > m     = 0 : t m xs
          | otherwise = (fromInteger m') : t r xs where (m',r) = divMod m x
-- Reinhard Zumkeller, May 08 2011