A111434 Numbers k such that the sums of the digits of k, k^2 and k^3 coincide.

0, 1, 10, 100, 468, 585, 1000, 4680, 5850, 5851, 5868, 10000, 28845, 46800, 58500, 58510, 58680, 58968, 100000, 288450, 468000, 585000, 585100, 586800, 589680, 1000000, 2884500, 4680000, 5850000, 5851000, 5868000, 5896800, 10000000

Offset

1,3

Comments

The sequence is clearly infinite, since we can add trailing zeros. Is the subset of values not ending in 0 infinite too (see A114135)?

Links

David A. Corneth, Table of n, a(n) for n = 1..1124 (using the b-file in A114135).

Example

468 is in the sequence since 468^2 = 219024 and 468^3 = 102503232 and we have 18 = 4+6+8 = 2+1+9+0+2+4 = 1+0+2+5+0+3+2+3+2.
5851 is in the sequence because 5851, 34234201 (= 5851^2) and 200304310051 (=5851^3) all have digital sum 19.

Maple

s:=proc(n) local nn: nn:=convert(n, base, 10): sum(nn[j], j=1..nops(nn)): end: a:=proc(n) if s(n)=s(n^2) and s(n)=s(n^3) then n else fi end: seq(a(n), n=0..1000000); # Emeric Deutsch, May 13 2006

Mathematica

SumOfDig[n_]:=Apply[Plus, IntegerDigits[n]]; Do[s=SumOfDig[n]; If[s==SumOfDig[n^2] && s==SumOfDig[n^3], Print[n]], {n, 10^6}]
Select[Range[0, 10000000], Length[Union[Total/@IntegerDigits[{#, #^2, #^3}]]] == 1&] (* Harvey P. Dale, Apr 26 2014 *)

Crossrefs

Cf. A011557, A058369, A070276.

Sequence in context: A208144 A207713 A222716 * A364342 A208074 A092707

Adjacent sequences: A111431 A111432 A111433 * A111435 A111436 A111437

Keyword

base,nonn

Author

Giovanni Resta, Nov 21 2005

Extensions

b-file Corrected by David A. Corneth, Jul 22 2021

Status

approved