A281148 - OEIS

%I #41 Feb 27 2022 05:40:02

%S 2,3,8,9,13,14,22,33,44,52,72,77,87,92,222,322,622,7737,7878,30302,

%T 44449,72777,844844,44744744

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

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

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

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

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

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

%Y Cf. A001014, A281678.

%K nonn,base,more

%O 1,1

%A _Robert Israel_ and _Altug Alkan_, Jan 27 2017