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%I #22 Jul 21 2021 00:43:09
%S 1,2,3,4,5,6,7,8,9,10,12,13,14,16,17,20,22,23,25,26,31,37,43
%N Numbers k such that the base-b expansion of k for each b = 3..k-1 never contains more than two distinct digits.
%C Conjecture: The sequence is finite, with 43 being the last term.
%C I checked the conjecture to 10809638.
%e 10 is a term of the sequence, since the base-b expansions of 10 for b = 3..9 are 101, 22, 20, 14, 13, 12, 11, respectively, and none of those expansions contain more than two distinct digits.
%t Select[Range@ 100, Max@ Table[Length@ Union@ IntegerDigits[#, b], {b, 3, # - 1}] <= 2 &] (* _Michael De Vlieger_, Feb 15 2019 *)
%o (PARI) is(n) = for(b=3, n-1, my(d=digits(n, b)); if(#vecsort(d, , 8) > 2, return(0))); 1
%K nonn,base,more
%O 1,2
%A _Felix Fröhlich_, Feb 14 2019