This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A385332 #14 Jul 01 2025 10:53:43
%S A385332 1,2,3,5,6,11,17,68,121,786
%N A385332 Integers k such that the set {k, k^2, ..., k^9} contains at least 8 zeroless numbers.
%C A385332 1, 2, 3, 6 and 68 are the only integers less than 3.3*10^16 such that {k, k^2,..., k^8} are all zeroless (See A124649), but of them 1^9, 2^9 and 3^9 are the only zeroless ones. If we weaken the condition and ask that 8 of the 9 numbers in the set {k, k^2,..., k^9} are zeroless, then more numbers appear that satisfy this property.
%C A385332 Is a(10) = 786 the largest term?
%e A385332 5 is a term, since the first nine powers of 5 are: 5, 25, 125, 625, 3125, 15625, 78125, 390625 and 1953125, where 8 of the 9 are zeroless.
%p A385332 zless:= n -> not has(convert(n,base,10),0):
%p A385332 filter:= proc(n) local i; nops(select(zless, [seq(n^i,i=1..9)]))>=8 end proc:
%p A385332 select(filter, [$1..1000]); # _Robert Israel_, Jun 26 2025
%t A385332 Select[Range[10^5],Total[Boole/@Positive/@Min/@IntegerDigits/@(#^Range[9])]>7&] (* _James C. McMahon_, Jul 01 2025 *)
%Y A385332 Cf. A124648, A124649.
%K A385332 nonn,base,more
%O A385332 1,2
%A A385332 _Gonzalo MartÃnez_, Jun 25 2025