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A068953
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Number of bases B (2 <= B <= n) such that every digit of n in base B is 0 or 1.
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6
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0, 1, 2, 3, 3, 3, 3, 3, 4, 4, 3, 4, 4, 3, 3, 4, 4, 3, 3, 4, 4, 3, 3, 3, 4, 4, 4, 4, 3, 5, 5, 3, 3, 3, 3, 5, 5, 3, 4, 4, 3, 4, 4, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 5, 5, 3, 3, 4, 4, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 4, 6, 5, 3, 5, 5, 3, 3, 3, 3, 5, 5, 3, 4, 4, 3, 3, 3, 3, 3, 4, 4, 3, 3
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OFFSET
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1,3
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COMMENTS
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All such bases are divisors of n or n-1, since the lowest base-B digit of n is 0 iff B | n, 1 iff B | n-1. - Robert Israel, Jul 04 2018
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LINKS
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EXAMPLE
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a(30)=5, since 30 written in the 5 bases 2, 3, 5, 29, 30 is 11110, 1010, 110, 11, 10.
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MAPLE
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f:= n ->
nops(select(b -> convert(convert(n, base, b), set) subset {0, 1}, {$2..n} intersect (numtheory:-divisors(n) union numtheory:-divisors(n-1)))):
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MATHEMATICA
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a[1]=0; a[n_] := Length[Select[Rest[Union[Divisors[n], Divisors[n-1]]], Max@@IntegerDigits[n, # ]==1&]]
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PROG
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(PARI) a(n) = sum(b=2, n, #select(x->(x>1), digits(n, b)) == 0); \\ Michel Marcus, Jul 04 2018
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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