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A168046 Characteristic function of zerofree numbers in decimal representation. 26

%I

%S 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,

%T 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,

%U 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

%N Characteristic function of zerofree numbers in decimal representation.

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

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

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

%C a(A007602(n)) = a(A038186(n)) = 1. - _Reinhard Zumkeller_, Apr 07 2011

%H R. Zumkeller, <a href="/A168046/b168046.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Zerofree.html">Zerofree</a>

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

%F From _Hieronymus Fischer_, Jan 23 2013: (Start)

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

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

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

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

%F 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)))).

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

%F (End)

%o (Haskell)

%o a168046 = fromEnum . ch0 where

%o ch0 x = x > 0 && (x < 10 || d > 0 && ch0 x') where (x', d) = divMod x 10

%o -- _Reinhard Zumkeller_, May 10 2015, Apr 07 2011

%Y Cf. A052382, A217096, A011540.

%K base,nonn

%O 0,1

%A _Reinhard Zumkeller_, Dec 01 2009

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Last modified February 20 20:55 EST 2019. Contains 320345 sequences. (Running on oeis4.)