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A364049 a(n) is the least k such that the base-n digits of 2^k are not all distinct.

%I A364049 #23 Jul 07 2023 05:48:36
%S A364049 2,2,4,5,6,3,6,11,16,14,11,12,8,4,8,15,16,12,16,18,9,17,15,14,24,13,
%T A364049 16,15,10,5,10,19,24,14,21,15,18,15,19,17,17,28,18,12,24,23,31,24,31,
%U A364049 20,26,44,35,33,25,18,36,14,14,18,12,6,12,23,45,37,38,24,20,35,36,26,51,31,33,47,34,34
%N A364049 a(n) is the least k such that the base-n digits of 2^k are not all distinct.
%H A364049 Robert Israel, <a href="/A364049/b364049.txt">Table of n, a(n) for n = 2..10000</a>
%e A364049 a(10) = 16 because 2^16 = 65536 does not have all distinct digits in base 10, while 2^k does have all distinct digits for 1 <= k <= 15.
%p A364049 f:= proc(n) local k,L;
%p A364049   for k from 2 do
%p A364049     L:= convert(2^k,base,n);
%p A364049     if nops(L) <> nops(convert(L,set)) then return k fi
%p A364049   od;
%p A364049 end proc:
%p A364049 map(f, [$2..100]);
%o A364049 (Python)
%o A364049 from itertools import count
%o A364049 from sympy.ntheory import digits
%o A364049 def a(n): return next(k for k in count(2) if len(set(d:=digits(1<<k,n)[1:]))<len(d))
%o A364049 print([a(n) for n in range(2, 80)]) # _Michael S. Branicky_, Jul 05 2023
%Y A364049 Cf. A004642, A004643, A000866, A004645, A004646, A004647, A001357, A000079, A011557, A364052, A364089.
%K A364049 nonn,base
%O A364049 2,1
%A A364049 _Robert Israel_, Jul 03 2023