

A068953


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


6



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

All such bases are divisors of n or n1, since the lowest baseB digit of n is 0 iff B  n, 1 iff B  n1.  Robert Israel, Jul 04 2018


LINKS



EXAMPLE

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


MAPLE

f:= n >
nops(select(b > convert(convert(n, base, b), set) subset {0, 1}, {$2..n} intersect (numtheory:divisors(n) union numtheory:divisors(n1)))):


MATHEMATICA

a[1]=0; a[n_] := Length[Select[Rest[Union[Divisors[n], Divisors[n1]]], Max@@IntegerDigits[n, # ]==1&]]


PROG

(PARI) a(n) = sum(b=2, n, #select(x>(x>1), digits(n, b)) == 0); \\ Michel Marcus, Jul 04 2018


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



