A281148 Numbers k such that k and k^6 have no digits in common.

2, 3, 8, 9, 13, 14, 22, 33, 44, 52, 72, 77, 87, 92, 222, 322, 622, 7737, 7878, 30302, 44449, 72777, 844844, 44744744

Offset: 1

Author

Robert Israel and Altug Alkan, Jan 27 2017

Keywords

• nonn
• base
• more

Comments

0, 1, 5, 6 cannot be the last digit of any term. [0 added to list by Jon E. Schoenfield, Jan 29 2017]

The only terms with no repeated digits are 2, 3, 8, 9, 13, 14, 52, 72, 87, 92.

If it exists, a(25) > 10^17. - David Radcliffe, May 26 2025

Examples

			92 is a term because 92^6 = 606355001344 has no digit 2 or 9.
		

Crossrefs

Cf. A001014, A281678.

Programs

Mathematica

fQ[n_] := Intersection[IntegerDigits[n], IntegerDigits[n^6]] == {}; Select[ Range@45000000, Mod[#, 5] > 1 && fQ@# &] (* Robert G. Wilson v, Jan 29 2017 *)

PARI

isok(n) = #setintersect(Set(digits(n)), Set(digits(n^6))) == 0;