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Numbers k that have no digits in common with k^7.
1

%I #32 Aug 19 2021 21:24:56

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

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

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

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

%C In this sequence, the only terms with no repeated digits are 3, 7, 8, 43, 93. - _Altug Alkan_, Jan 26 2017

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

%p select(t -> convert(convert(t,base,10),set) intersect convert(convert(t^7,base,10),set) = {},

%p {seq(seq(10*i+j,j=[2,3,7,8]),i=0..10^4});

%t Select[Range[40000], Intersection[IntegerDigits[#], IntegerDigits[ #^7]] == {}&] (* _Vincenzo Librandi_, Jan 27 2017 *)

%o (PARI) isok(n) = #setintersect(Set(digits(n)), Set(digits(n^7))) == 0; \\ _Michel Marcus_, Jan 26 2017

%Y Cf. A001015. Contains A253576.

%Y Cf. A281148.

%K nonn,more,base

%O 1,1

%A _Robert Israel_, Jan 26 2017