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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

Index entries for characteristic functions

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: A249832 A240355 A217096 * A185119 A280130 A279760

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 February 17 20:06 EST 2018. Contains 299296 sequences. (Running on oeis4.)