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

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

Offset

1,3

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

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(n-1)))):
map(f, [$1..200]); # Robert Israel, Jul 04 2018

Mathematica

a[1]=0; a[n_] := Length[Select[Rest[Union[Divisors[n], Divisors[n-1]]], 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

Cf. A059972.

Sequence in context: A347744 A361197 A320110 * A362960 A189635 A109785

Adjacent sequences: A068950 A068951 A068952 * A068954 A068955 A068956

Keyword

nonn,base

Author

Dean Hickerson, Mar 31 2002

Status

approved