A067075 a(n) is the smallest number m such that the sum of the digits of m^3 is equal to n^3.

0, 1, 2, 27, 1192, 341075, 3848163483, 2064403725539899

Offset: 0

Author

Amarnath Murthy, Jan 05 2002

Keywords

• nonn
• base
• more

Comments

If n = 6*k, a(n) <= A002283(n^3/18). For example, a(6) = 3848163483 <= A002283(6^3/18) = 999999999999. - Seiichi Manyama, Aug 12 2017

a(n) >= ceiling(A051885(n^3)^(1/3)). For example a(7) >= ceiling(A051885(7^3)^(1/3)) = ceiling((2*10^38-1)^(1/3)) = 5848035476426 - David A. Corneth, Aug 23 2018

From Zhining Yang, Jun 20 2024: (Start)

a(8) <= 99995999799995999999999.

a(9) <= 999699989999999949999999999999999.

a(10) <= 199999999929999999999949999999999999999999999.

(End)

Examples

			a(3) = 27 as 27^3 = 19683 is the smallest cube whose digit sum = 27 = 3^3.
		

Crossrefs

Cf. A051885, A061912, A067074. Subsequence of A067177.

Programs

Mathematica

Do[k = 1; While[Plus @@ IntegerDigits[k^3] != n^3, k++ ]; Print[k], {n, 1, 6}] (* Ryan Propper, Jul 07 2005 *)

PARI

a(n) = my(k=0); while (sumdigits(k^3) != n^3, k++); k; \\ Seiichi Manyama, Aug 12 2017

Extensions

Corrected and extended by Ryan Propper, Jul 07 2005

a(0)=0 prepended by Seiichi Manyama, Aug 12 2017

a(7) from Zhining Yang, Jun 20 2024