A383347 Numbers that have the same set of digits as the sum of the cubes of their digits.

0, 1, 135, 137, 153, 173, 307, 315, 317, 351, 370, 371, 407, 470, 513, 531, 703, 704, 713, 730, 731, 740, 3007, 3070, 3700, 4007, 4070, 4700, 7003, 7004, 7030, 7040, 7300, 7400, 11112, 11113, 11121, 11131, 11211, 11311, 12111, 12599, 12959, 12995, 13111, 15299

Offset: 1

Author

Jean-Marc Rebert, Apr 24 2025

Keywords

• nonn
• base

Comments

Contains 3*10^j + 7*10^k and 4*10^j + 7*10^k if j <> k and max(j,k) >= 2. - Robert Israel, Apr 25 2025

Examples

			135 and 1^3 + 3^3 + 5^3 = 153 have the same set of digits {1,3,5}, so 135 is a term.
		

Crossrefs

Cf. A055012, A249515.

Cf. A046197 (a subsequence).

Programs

Maple

filter:= proc(n) local L,t;
  L:= convert(n,base,10);
  convert(L,set) = convert(convert(add(t^3,t=L),base,10),set)
end proc:
select(filter, [$0 .. 10^5]); # Robert Israel, Apr 25 2025

Mathematica

q[k_] := Module[{d = IntegerDigits[k]}, Union[d] == Union[IntegerDigits[Total[d^3]]]]; Select[Range[0, 16000], q] (* Amiram Eldar, Apr 24 2025 *)

PARI

isok(k) = my(d=digits(k)); Set(d) == Set(digits(sum(i=1, #d, d[i]^3))); \\ Michel Marcus, Apr 24 2025

Python

def ok(n): return set(s:=str(n)) == set(str(sum(int(d)**3 for d in s)))
print([k for k in range(2*10**4) if ok(k)]) # Michael S. Branicky, Apr 24 2025