A281678 Numbers k that have no digits in common with k^7.

3, 7, 8, 33, 43, 77, 93, 272, 332, 662, 7757, 31333

Offset: 1

Author

Robert Israel, Jan 26 2017

Keywords

• nonn
• more
• base

Comments

All terms have last digit 2, 3, 7 or 8.

Sequence is likely to be finite. If it exists, a(13) > 10^7.

In this sequence, the only terms with no repeated digits are 3, 7, 8, 43, 93. - Altug Alkan, Jan 26 2017

If it exists, a(13) > 10^17. - David Radcliffe, May 26 2025

Examples

			43 is a term because 43^7 = 271818611107 has no digit 4 or 3.
		

Crossrefs

Cf. A001015. Contains A253576.

Cf. A281148.

Programs

Maple

select(t -> convert(convert(t,base,10),set) intersect convert(convert(t^7,base,10),set) = {},
{seq(seq(10*i+j,j=[2,3,7,8]),i=0..10^4});

Mathematica

Select[Range[40000], Intersection[IntegerDigits[#], IntegerDigits[ #^7]] == {}&] (* Vincenzo Librandi, Jan 27 2017 *)

PARI

isok(n) = #setintersect(Set(digits(n)), Set(digits(n^7))) == 0; \\ Michel Marcus, Jan 26 2017