A113951 -id:A113951 - cp's OEIS frontend

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

2, 3, 7, 8, 22, 27, 43, 47, 48, 52, 53, 63, 68, 77, 92, 157, 172, 177, 187, 188, 192, 222, 223, 252, 263, 303, 378, 408, 423, 442, 458, 468, 477, 478, 487, 527, 552, 558, 577, 587, 588, 608, 648, 692, 707, 772, 808, 818, 823, 843, 888, 918, 922

Offset: 1

Patrick De Geest

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

Might be called "Exclusionary Cubes", although this might be reserved for terms having no duplicate digits, cf. link to rec.puzzles discussion group. In that case the largest term would be 7658 = A113951(3). - M. F. Hasler, Oct 17 2018; corrected thanks to David Radcliffe and Michel Marcus, Apr 30 2020

			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

Giovanni Resta, Table of n, a(n) for n = 1..1699 (terms < 10^19, first 528 terms from Charles R Greathouse IV)
Cliff Pickover et al, Exclusionary Squares and Cubes, rec.puzzles topic on google groups, January 2002

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

Select[Range[5000], Intersection[IntegerDigits[#], IntegerDigits[#^3]]=={}&] (* Vincenzo Librandi, Oct 04 2013 *)

is(n)=my(d=Set(digits(n))); setminus(d,Set(digits(n^3)))==d \\ Charles R Greathouse IV, Oct 02 2013

is_A029785(n)=setintersect(Set(digits(n)),Set(digits(n^3)))==[] \\ M. F. Hasler, Oct 16 2018

Name reworded by Jon E. Schoenfield and M. F. Hasler, Oct 16 2018

A109135 Least number whose n-th power is exclusionary (or 0 if no such n exists). An exclusionary n-th power m^n is one made up of digits not appearing in m, which itself consists of distinct digits.

Original entry on oeis.org

0, 2, 2, 2, 0, 2, 3, 3, 0, 3, 3, 2, 0, 2, 0, 2, 0, 0, 3, 2, 0, 2, 2, 7, 0, 2, 3, 3, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 3, 0, 2, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 2

Lekraj Beedassy, Aug 17 2005

a(n)=0 for n=1(mod 4)=A016813.

a(4k+1) = 0. All other zeros are unproved and have been checked up to m = 1000. - David Wasserman, May 27 2008

H. Ibstedt, Solution to Problem 2623, "Exclusionary Powers", pp. 346-9 Journal of Recreational Mathematics, Vol. 32 No.4 2003-4 Baywood NY.

Cf. A113951.

More terms from David Wasserman, May 27 2008

A113952 Largest exclusionary n-th power (or 0 if no such number exists).

Original entry on oeis.org

408540845584, 449103134312, 51050010415041, 0, 606355001344, 60170087060757, 66045000696445844586496, 0, 3570467226624, 743008370688, 16777216, 0, 9012061295995008299689, 0, 1853020188851841, 0, 0, 1162261467, 1099511627776

Offset: 2

Lekraj Beedassy, Nov 09 2005

An exclusionary n-th power m^n is one made up of digits not appearing in the root m which itself consists of distinct digits. For the corresponding root m, see A113951. In principle, no exclusionary n-th power exists for n=1(mod 4)=A016813.

			a(10)=3570467226624 because it shares no digit in common with its 10th root 18 and no number with distinct digits greater than 18 exhibits such property.

H. Ibstedt, Solution to Problem 2623, "Exclusionary Powers", pp. 346-9 Journal of Recreational Mathematics, Vol. 32 No.4 2003-4 Baywood NY.

Shyam Sunder Gupta, Elegance of Squares, Cubes, and Higher Powers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 2, 29-81.

Cf. A112735, A112993, A113317.

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

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A109135 Least number whose n-th power is exclusionary (or 0 if no such n exists). An exclusionary n-th power m^n is one made up of digits not appearing in m, which itself consists of distinct digits.

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A113952 Largest exclusionary n-th power (or 0 if no such number exists).

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