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A029785 Numbers k whose cube k^3 has no digit in common with k. 9


%S 2,3,7,8,22,27,43,47,48,52,53,63,68,77,92,157,172,177,187,188,192,222,

%T 223,252,263,303,378,408,423,442,458,468,477,478,487,527,552,558,577,

%U 587,588,608,648,692,707,772,808,818,823,843,888,918,922

%N Numbers k whose cube k^3 has no digit in common with k.

%C Original name: Digits of n are not present in n^3.

%C Might be called "Exclusionary Cubes", although this might be reserved for terms having no duplicate digits, cf. link to rec.puzzles discussion group. Then the largest term would be 639172. - _M. F. Hasler_, Oct 17 2018

%H Giovanni Resta, <a href="/A029785/b029785.txt">Table of n, a(n) for n = 1..1699</a> (terms < 10^19, first 528 terms from Charles R Greathouse IV)

%H Cliff Pickover et al, <a href="https://groups.google.com/forum/#!topic/rec.puzzles/ubSItPD_DGY">Exclusionary Squares and Cubes</a>, rec.puzzles topic on google groups, January 2002

%e k = 80800000008880080808880080088 is in the sequence because the 87-digit number k^3 has only digits 1, ..., 7 and 9. - _M. F. Hasler_, Oct 16 2018

%t Select[Range[5000], Intersection[IntegerDigits[#], IntegerDigits[#^3]]=={}&] (* _Vincenzo Librandi_, Oct 04 2013 *)

%o (PARI) is(n)=my(d=Set(digits(n))); setminus(d,Set(digits(n^3)))==d \\ _Charles R Greathouse IV_, Oct 02 2013

%o (PARI) is_A029785(n)=setintersect(Set(digits(n)),Set(digits(n^3)))==[] \\ _M. F. Hasler_, Oct 16 2018

%Y Cf. A029786, A029783, A029784, A111116, A113316.

%K nonn,base

%O 1,1

%A _Patrick De Geest_

%E Name reworded by _Jon E. Schoenfield_ and _M. F. Hasler_, Oct 16 2018

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Last modified January 22 05:11 EST 2019. Contains 319353 sequences. (Running on oeis4.)