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

Author

Patrick De Geest

Keywords

• nonn
• base

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

Examples

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

Links

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

Crossrefs

Cf. A029793, A029797, A232659-A232662.

Programs

Magma

[ n: n in [0..8*10^6] | Set(Intseq(n)) eq Set(Intseq(n^3)) ];  // Bruno Berselli, Jun 28 2011

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 *)

PARI

isA029795(n)=Set(Vec(Str(n)))==Set(Vec(Str(n^3))) \\ Charles R Greathouse IV, Jun 28 2011