A168046 Characteristic function of zerofree numbers in decimal representation.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0

Offset: 0

Author

Reinhard Zumkeller, Dec 01 2009

Keywords

• base
• nonn

Comments

a(A052382(n)) = 1; a(A011540(n)) = 0;

a(n) = A000007(A055641(n));

not the same as A168184: a(n)=A168184(n) for n<=100.

a(A007602(n)) = a(A038186(n)) = 1. - Reinhard Zumkeller, Apr 07 2011

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Zerofree
• Index entries for characteristic functions

Crossrefs

Cf. A052382, A217096, A011540.

Programs

Haskell

a168046 = fromEnum . ch0 where
   ch0 x = x > 0 && (x < 10 || d > 0 && ch0 x') where (x', d) = divMod x 10
-- Reinhard Zumkeller, May 10 2015, Apr 07 2011

Mathematica

Map[Boole[FreeQ[IntegerDigits[#], 0]] &, Range[0, 100]] (* Paolo Xausa, May 06 2024 *)

Formula

a(n) = A057427(A010879(n)) * (if n<10 then 1 else a(A059995(n))).

From Hieronymus Fischer, Jan 23 2013: (Start)

a(n) = A057427(A007954(n)) = sign(dp_10(n)).

where dp_10(n) digital product of n in base 10.

a(n) = 1 - A217096(n).

a(n) = 1 - sign(A055641(n)).

g(x) = x(1-x^9)/((1-x)(1-x^10))(1 + sum_{j>=1} (x^((10^j-10)/9) - x^10^j)/(1-x^10^(j+1)))).

g(x) = 1/(1-x) - g_A217096(x), where g_A217096(x) is the g.f. of A217096.

(End)