A067075 - OEIS

%I #40 Jun 21 2024 03:50:39

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

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

%C 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

%C 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

%C From _Zhining Yang_, Jun 20 2024: (Start)

%C a(8) <= 99995999799995999999999.

%C a(9) <= 999699989999999949999999999999999.

%C a(10) <= 199999999929999999999949999999999999999999999.

%C (End)

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

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

%o (PARI) a(n) = my(k=0); while (sumdigits(k^3) != n^3, k++); k; \\ _Seiichi Manyama_, Aug 12 2017

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

%K nonn,base,more

%O 0,3

%A _Amarnath Murthy_, Jan 05 2002

%E Corrected and extended by _Ryan Propper_, Jul 07 2005

%E a(0)=0 prepended by _Seiichi Manyama_, Aug 12 2017

%E a(7) from _Zhining Yang_, Jun 20 2024