%I #16 Jul 20 2024 10:53:48
%S 1,1,3,4,5,8,5,10,29,19,19,19,16,18,7,43,41,37,45,39,55,33,43,60,35,
%T 61,56,50,44,69,9,64,44,80,43,88,53,71,56,68,59,78,76,74,95,109,111,
%U 81,86,136,117,75,98,83,84,99,104,116,95,118,60,81,11,119,119,172,140,97,105,113,93,122,92
%N a(n) is the greatest k such that the base-n digits of 2^k are all distinct.
%C a(n) <= log_2(A062813(n)).
%e a(10) = 29 because all decimal digits of 2^29 = 536870912 are distinct.
%p f:= proc(b) local M,k,L;
%p M:= b^b - (b^b-b)/(b-1)^2;
%p for k from ilog2(M) to 1 by -1 do
%p L:= convert(2^k,base,b);
%p if nops(L) = nops(convert(L,set)) then return k fi
%p od
%p end proc:
%p map(f, [$2..100]);
%o (Python)
%o from sympy.ntheory.factor_ import digits
%o def A364089(n):
%o m = 1<<(l:=((r:=n**n)-(r-n)//(n-1)**2).bit_length()-1)
%o while len(d:=digits(m,n)[1:]) > len(set(d)):
%o l -= 1
%o m >>= 1
%o return l # _Chai Wah Wu_, Jul 07 2023
%Y Cf. A004642, A004643, A000866, A004645, A004646, A004647, A001357, A000079, A364049.
%K nonn,base
%O 2,3
%A _Robert Israel_, Jul 04 2023