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A217096 Characteristic function of numbers that have a nonleading zero in their decimal representation (A011540). 0 itself is also included, so a(0) = 1. 3

%I

%S 1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,

%T 0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,

%U 0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0

%N Characteristic function of numbers that have a nonleading zero in their decimal representation (A011540). 0 itself is also included, so a(0) = 1.

%H Antti Karttunen, <a href="/A217096/b217096.txt">Table of n, a(n) for n = 0..5000</a>

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

%F a(n) = 1 - A057427(A007954(n)) = 1 - sign(dp_10(n)).

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

%F a(n) = 1 - A168046(n).

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

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

%F g(x) = 1/(1-x) - g_A168046(x), where g_A168046 (x) is the g.f. of A168046.

%t Table[Boole[MemberQ[IntegerDigits[n], 0]], {n, 0, 109}] (* _Alonso del Arte_, Feb 02 2013 *)

%o (PARI) A217096(n) = if(!n,1,0==(vecsort(digits(n),,8)[1])); \\ _Antti Karttunen_, Dec 07 2017

%Y Cf. A011540, A055641, A168046, A209929.

%K nonn,base

%O 0

%A _Hieronymus Fischer_, Jan 23 2013

%E Name edited by _Antti Karttunen_, Dec 07 2017

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Last modified April 25 18:12 EDT 2019. Contains 322461 sequences. (Running on oeis4.)