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A068953 Number of bases B (2 <= B <= n) such that every digit of n in base B is 0 or 1. 5

%I

%S 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,

%T 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,

%U 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

%N Number of bases B (2 <= B <= n) such that every digit of n in base B is 0 or 1.

%C 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

%H Robert Israel, <a href="/A068953/b068953.txt">Table of n, a(n) for n = 1..10000</a>

%e a(30)=5, since 30 written in the 5 bases 2, 3, 5, 29, 30 is 11110, 1010, 110, 11, 10.

%p f:= n ->

%p nops(select(b -> convert(convert(n,base,b),set) subset {0,1}, {$2..n} intersect (numtheory:-divisors(n) union numtheory:-divisors(n-1)))):

%p map(f, [$1..200]); # _Robert Israel_, Jul 04 2018

%t a[1]=0; a[n_] := Length[Select[Rest[Union[Divisors[n], Divisors[n-1]]], Max@@IntegerDigits[n, # ]==1&]]

%o (PARI) a(n) = sum(b=2, n, #select(x->(x>1), digits(n, b)) == 0); \\ _Michel Marcus_, Jul 04 2018

%Y Cf. A059972.

%K nonn,base

%O 1,3

%A _Dean Hickerson_, Mar 31 2002

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Last modified April 8 05:55 EDT 2020. Contains 333312 sequences. (Running on oeis4.)