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 A267142 The characteristic function of the multiples of 9. 2
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0 COMMENTS Decimal expansion of 100000000/999999999. Period 9: repeat [1, 0, 0, 0, 0, 0, 0, 0, 0]. More generally, the ordinary generating function for the characteristic function of the multiples of k is 1/(1 - x^k). LINKS Antti Karttunen, Table of n, a(n) for n = 0..999 FORMULA G.f.: 1/(1 - x^9). a(n) = abs(sign(n mod 9) - 1). a(n) = abs(A168182(n)-1). A007953(a(n)*n) mod 9 = 0. MATHEMATICA Table[Boole[Divisible[n, 9]], {n, 0, 115}] Table[Abs[Sign[Mod[n, 9]] - 1], {n, 0, 115}] CoefficientList[Series[1 / (1 - x^9), {x, 0, 100}], x] (* Vincenzo Librandi, Jan 11 2016 *) PROG (MAGMA) &cat[&cat[[1], [0]^^8]^^14]; // Vincenzo Librandi, Jan 11 2016 (PARI) a(n) = n\9 - (n-1)\9; \\ Altug Alkan, Jan 11 2016 (PARI) A267142(n) = !(n%9); \\ Antti Karttunen, Oct 07 2017 CROSSREFS Cf. A008591, A079978, A079979, A079998, A082784, A121262, A168182, A253513. Sequence in context: A014954 A015899 A015494 * A185119 A280130 A304002 Adjacent sequences:  A267139 A267140 A267141 * A267143 A267144 A267145 KEYWORD nonn,easy AUTHOR Ilya Gutkovskiy, Jan 11 2016 STATUS approved

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Last modified January 23 11:04 EST 2019. Contains 319391 sequences. (Running on oeis4.)