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A168185 Characteristic function of numbers that are not multiples of 12. 12
0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n+12) = a(n);

a(n) = A000007(A010881(n));

a(A168186(n)) = 1; a(A008594(n)) = 0;

A033444(n) = Sum_{k=0..n} a(k)*(n-k).

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for characteristic functions

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,1).

FORMULA

For the general case: the characteristic function of numbers that are not multiples of m is a(n) = floor((n-1)/m) - floor(n/m) + 1, m,n > 0. - Boris Putievskiy, May 08 2013

MAPLE

a:=n->`if`(modp(n, 12)=0, 0, 1); seq(a(n), n=0..150); # Muniru A Asiru, Sep 21 2018

MATHEMATICA

If[Divisible[#, 12], 0, 1]&/@Range[0, 120] (* Harvey P. Dale, Apr 03 2015 *)

PROG

(PARI) a(n)=!!(n%12) \\ Charles R Greathouse IV, Aug 21 2011

CROSSREFS

Cf. A010881, A145568, A168184, A168182, A168181, A109720, A097325, A011558, A166486, A011655, A000035.

Sequence in context: A339145 A011582 A145568 * A011583 A011584 A011585

Adjacent sequences: A168182 A168183 A168184 * A168186 A168187 A168188

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Nov 30 2009

STATUS

approved

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Last modified December 7 21:25 EST 2022. Contains 358669 sequences. (Running on oeis4.)