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A118470 Numbers k for which digitsum(k) + digitsum(k^2) + digitsum(k^3) = digitsum(k^4).

%I A118470 #35 Dec 26 2021 02:58:35
%S A118470 0,162,171,351,468,558,1620,1710,2106,3321,3510,4023,4680,5121,5247,
%T A118470 5544,5580,5868,8001,10008,10071,10224,10305,10503,10818,11025,11241,
%U A118470 11511,12321,12654,12888,13239,14004,14301,15471,15876,16011,16200,16218,17100
%N A118470 Numbers k for which digitsum(k) + digitsum(k^2) + digitsum(k^3) = digitsum(k^4).
%C A118470 If x is a term, then so is 10*x. - _Michael S. Branicky_, Dec 25 2021
%H A118470 J.W.L. (Jan) Eerland, <a href="/A118470/b118470.txt">Table of n, a(n) for n = 1..3721</a> (all terms < 10^7)
%e A118470 162 is a term because s(162) = 9, s(162^2) = 18, s(162^3) = 27, s(162^4) = 54 and 9 + 18 + 27 = 54.
%t A118470 Select[Range[0, 20000], Sum[i*(DigitCount[ # ][[i]] + DigitCount[ #^2][[i]] + DigitCount[ #^3][[i]]), {i, 1, 9}] == Sum[i*DigitCount[ #^4][[i]], {i, 1, 9}] &] (* _Stefan Steinerberger_, May 04 2006 *)
%t A118470 s[n_] := Plus @@ IntegerDigits@n; Select[ Range[0, 16217], s@# + s[ #^2] + s[ #^3] == s[ #^4] &] (* _Robert G. Wilson v_, May 04 2006 *)
%t A118470 Parallelize[While[True,If[Total[IntegerDigits[n]]+Total[IntegerDigits[n^2]]+Total[IntegerDigits[n^3]]==Total[IntegerDigits[n^4]],Print[n]];n++];n] (* _J.W.L. (Jan) Eerland_, Dec 25 2021 *)
%o A118470 (PARI) is(n)=my(s=sumdigits); s(n)+s(n^2)+s(n^3) == s(n^4) \\ _Anders Hellström_, Sep 16 2015
%o A118470 (PARI) select(isA118470(n)={sumdigits(n)+sumdigits(n^2)+sumdigits(n^3) == sumdigits(n^4)}, [0..1000]) \\ _J.W.L. (Jan) Eerland_, Dec 25 2021
%o A118470 (Python)
%o A118470 def sd(n): return sum(map(int, str(n)))
%o A118470 def ok(n): return sd(n) + sd(n**2) + sd(n**3) == sd(n**4)
%o A118470 print([k for k in range(20000) if ok(k)]) # _Michael S. Branicky_, Dec 25 2021
%Y A118470 Cf. A007953, A004159, A004164, A055565.
%K A118470 nonn,base
%O A118470 1,2
%A A118470 Luc Stevens (lms022(AT)yahoo.com), May 04 2006
%E A118470 More terms from _Joshua Zucker_, May 11 2006