cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

Views

Author

Giovanni Resta, Nov 21 2005

Keywords

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)?

Examples

			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.
		

Crossrefs

Programs

  • 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 *)

Extensions

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