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A111434 Numbers n such that the sums of the digits of n, n^2 and n^3 coincide. 5
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 (list; graph; refs; listen; history; text; internal format)
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

Robert G. Wilson v, Table of n, a(n) for n = 1..917

EXAMPLE

468 is in the sequence since 468^2=219024and 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. A058369, A070276.

Sequence in context: A208144 A207713 A222716 * A208074 A092707 A224263

Adjacent sequences:  A111431 A111432 A111433 * A111435 A111436 A111437

KEYWORD

base,nonn

AUTHOR

Giovanni Resta, Nov 21 2005

STATUS

approved

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Last modified May 25 12:30 EDT 2019. Contains 323568 sequences. (Running on oeis4.)