A164883 Cubes with the property that the sum of the cubes of the digits is also a cube.

0, 1, 8, 1000, 8000, 474552, 1000000, 1643032, 8000000, 13312053, 27818127, 125751501, 474552000, 1000000000, 1015075125, 1121622319, 1256216039, 1501123625, 1643032000, 3811036328, 8000000000, 11000295424, 13312053000

Offset

1,3

Comments

It is known (Murthy 2001) that the sequence is infinite. (1) The number {3(10^(k+2)+1)}^3 for all k produces such numbers. (2) Less trivially, {10^(n+2) - 4}^3 is a member of this sequence for n = 4*{(10^(3k)-1)/27}-1, for all k, for which the sum of the cubes of the digits is {6*10^k}^3.

References

Amarnath Murthy, Smarandache Fermat Additive Cubic Sequence, 2011. (To be published in the Smarandache Notions Journal.)

Links

Table of n, a(n) for n=1..23.

Example

474552 = 78^3 is a term since 4^3+7^3+4^3+5^3+5^3+2^3 = 729 = 9^3.

Mathematica

Select[Range[0, 2500]^3, IntegerQ[Total[IntegerDigits[#]^3]^(1/3)]&] (* Harvey P. Dale, Jun 03 2012 *)

Crossrefs

Sequence in context: A061105 A118545 A017091 * A019545 A046242 A260028

Adjacent sequences: A164880 A164881 A164882 * A164884 A164885 A164886

Keyword

nonn,base

Author

Amarnath Murthy, Apr 21 2001

Extensions

Corrected and extended by Gaurav Kumar, Aug 29 2009

Status

approved