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A306424
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Numbers k such that the base-b expansion of k for each b = 3..k-1 never contains more than two distinct digits.
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0
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 16, 17, 20, 22, 23, 25, 26, 31, 37, 43
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OFFSET
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1,2
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COMMENTS
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Conjecture: The sequence is finite, with 43 being the last term.
I checked the conjecture to 10809638.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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Select[Range@ 100, Max@ Table[Length@ Union@ IntegerDigits[#, b], {b, 3, # - 1}] <= 2 &] (* Michael De Vlieger, Feb 15 2019 *)
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PROG
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(PARI) is(n) = for(b=3, n-1, my(d=digits(n, b)); if(#vecsort(d, , 8) > 2, return(0))); 1
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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STATUS
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approved
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