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A168046 Characteristic function of zerofree numbers in decimal representation. 26
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 (list; graph; refs; listen; history; text; internal format)
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

R. Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for characteristic functions

Eric Weisstein's World of Mathematics, Zerofree

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)

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

CROSSREFS

Cf. A052382, A217096, A011540.

Sequence in context: A168181 A164980 A168182 * A168184 A013595 A011582

Adjacent sequences:  A168043 A168044 A168045 * A168047 A168048 A168049

KEYWORD

base,nonn

AUTHOR

Reinhard Zumkeller, Dec 01 2009

STATUS

approved

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Last modified October 19 16:07 EDT 2018. Contains 316366 sequences. (Running on oeis4.)