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

Author

Patrick De Geest

Keywords

• nonn
• base

Comments

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

Examples

			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
		

Links

• 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

Crossrefs

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

Programs

Mathematica

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

PARI

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

PARI

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

Extensions

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