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A029785
Numbers k whose cube k^3 has no digit in common with k.
9
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
1,1
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
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
EXAMPLE
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
MATHEMATICA
Select[Range[5000], Intersection[IntegerDigits[#], IntegerDigits[#^3]]=={}&] (* Vincenzo Librandi, Oct 04 2013 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,base
EXTENSIONS
Name reworded by Jon E. Schoenfield and M. F. Hasler, Oct 16 2018
STATUS
approved