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

0,1

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

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)

Mathematica

Map[Boole[FreeQ[IntegerDigits[#], 0]] &, Range[0, 100]] (* Paolo Xausa, May 06 2024 *)
Table[If[DigitCount[n, 10, 0]==0, 1, 0], {n, 0, 120}] (* Harvey P. Dale, Nov 16 2025 *)

Prog

(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
(Python)
def A168046(n): return int(not '0' in str(n)) # Chai Wah Wu, Oct 09 2025

Crossrefs

Cf. A052382, A217096, A011540.

Sequence in context: A204447 A368905 A188642 * A168184 A013595 A339145

Adjacent sequences: A168043 A168044 A168045 * A168047 A168048 A168049

Keyword

base,nonn

Author

Reinhard Zumkeller, Dec 01 2009

Status

approved