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A267142 The characteristic function of the multiples of 9. 2

%I

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

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

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

%N The characteristic function of the multiples of 9.

%C Decimal expansion of 100000000/999999999.

%C Period 9: repeat [1, 0, 0, 0, 0, 0, 0, 0, 0].

%C More generally, the ordinary generating function for the characteristic function of the multiples of k is 1/(1 - x^k).

%H Antti Karttunen, <a href="/A267142/b267142.txt">Table of n, a(n) for n = 0..999</a>

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

%F G.f.: 1/(1 - x^9).

%F a(n) = abs(sign(n mod 9) - 1).

%F a(n) = abs(A168182(n)-1).

%F A007953(a(n)*n) mod 9 = 0.

%t Table[Boole[Divisible[n, 9]], {n, 0, 115}]

%t Table[Abs[Sign[Mod[n, 9]] - 1], {n, 0, 115}]

%t CoefficientList[Series[1 / (1 - x^9), {x, 0, 100}], x] (* _Vincenzo Librandi_, Jan 11 2016 *)

%o (MAGMA) &cat[&cat[[1],[0]^^8]^^14]; // _Vincenzo Librandi_, Jan 11 2016

%o (PARI) a(n) = n\9 - (n-1)\9; \\ _Altug Alkan_, Jan 11 2016

%o (PARI) A267142(n) = !(n%9); \\ _Antti Karttunen_, Oct 07 2017

%Y Cf. A008591, A079978, A079979, A079998, A082784, A121262, A168182, A253513.

%K nonn,easy

%O 0

%A _Ilya Gutkovskiy_, Jan 11 2016

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Last modified February 24 14:41 EST 2018. Contains 299623 sequences. (Running on oeis4.)