A168185 Characteristic function of numbers that are not multiples of 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

Offset: 0

Author

Reinhard Zumkeller, Nov 30 2009

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

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 *)

PARI

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

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