A052072 Smallest cubes whose digits occur with the same frequency n.

0, 1331, 700227072, 22676697737363992239, 1728999927211172788179288, 256263633328535368685258882625, 19194114355415391344355399945943513, 2342441231418833141828248411332348812823

Offset: 1

Author

Patrick De Geest, Jan 15 2000

Keywords

• nonn
• base
• more
• nice

Examples

			22676697737363992239 (= 2830479^3) and its digits 2, 3, 6, 7 and 9 each occur four times.
		

Links

• Patrick De Geest, Numbers whose digits occur with same frequency

Crossrefs

Cf. A052071, A052047, A052048, A052051, A052052, A052070.

Programs

Mathematica

Table[i = 0;
While[x = i^3; Union@DeleteCases[DigitCount[x], 0] != {n}, i++];
x, {n, 7}] (* Robert Price, Oct 12 2019 *)
Select[Range[400]^3,Length[Union[DeleteCases[DigitCount[#],0]]]==1&] (* Harvey P. Dale, Apr 30 2022 *)

Python

def A052072(n):
    a, b, c = 0, 0, 0
    for i in range(10**9):
        s = str(c)
        for d in set(s):
            if s.count(d) != n:
                break
        else:
            return c
        c += a + b + 1
        b += 2*a + 3
        a += 3
    return 'search limit reached.'  # Chai Wah Wu, Aug 11 2015

Extensions

Offset corrected by Michel Marcus, Aug 12 2015

a(7) from Giovanni Resta, Aug 19 2018

a(8) from Mihael Tunik, May 26 2025