A029795 Numbers k such that k and k^3 have the same set of digits.

0, 1, 10, 100, 1000, 10000, 100000, 107624, 109573, 132485, 138624, 159406, 165640, 192574, 205738, 215806, 251894, 281536, 318725, 419375, 427863, 568314, 642510, 713960, 953867, 954086, 963218, 965760, 1000000, 1008529, 1023479

Offset

1,3

Comments

Conjecture: there exists some m and N for which a(n) = m + n for all n >= N. - Charles R Greathouse IV, Jun 28 2011

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..500

Example

109573^3 = 1315559990715517. Since both numbers use the digits 0, 1, 3, 5, 7, 9, and no others, 109573 is in the sequence.

Maple

seq(`if`(convert(convert(n, base, 10), set) = convert(convert(n^3, base, 10), set), n, NULL), n=0..500000); # Nathaniel Johnston, Jun 28 2011

Mathematica

Select[Range[0, 199999], Union[IntegerDigits[#]] == Union[IntegerDigits[#^3]] &] (* Alonso del Arte, Jan 12 2020 *)

Prog

(Magma) [ n: n in [0..8*10^6] | Set(Intseq(n)) eq Set(Intseq(n^3)) ];  // Bruno Berselli, Jun 28 2011
(PARI) isA029795(n)=Set(Vec(Str(n)))==Set(Vec(Str(n^3))) \\ Charles R Greathouse IV, Jun 28 2011

Crossrefs

Cf. A029793, A029797, A232659-A232662.

Sequence in context: A136837 A136854 A029778 * A136844 A136842 A136872

Adjacent sequences: A029792 A029793 A029794 * A029796 A029797 A029798

Keyword

nonn,base

Author

Patrick De Geest

Status

approved