A168184 Characteristic function of numbers that are not multiples of 10.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1

Offset: 0

Author

Reinhard Zumkeller, Nov 30 2009

Keywords

• nonn
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• Index entries for characteristic functions
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,1).

Crossrefs

Cf. A168185, A145568, A168182, A168181, A109720, A097325, A011558, A166486, A011655, A000035, A010690, A033442.

Programs

Haskell

a168184 = (1 -) . (0 ^) . (`mod` 10)
a168184_list = cycle [0,1,1,1,1,1,1,1,1,1]
-- Reinhard Zumkeller, Oct 10 2012

Mathematica

Table[If[Mod[n,10]==0,0,1],{n,0,110}] (* or *) PadRight[{},110,{0,1,1,1,1,1,1,1,1,1}] (* Harvey P. Dale, Jun 03 2023 *)

PARI

a(n)=n%10>0 \\ Charles R Greathouse IV, Sep 24 2015

Formula

a(n+10) = a(n);

a(n) = A000007(A010879(n));

a(A067251(n)) = 1; a(A008592(n)) = 0;

not the same as A168046: a(n)=A168046 for n<=100;

A033442(n) = Sum_{k=0..n} a(k)*(n-k).

Dirichlet g.f.: (1-1/10^s)*zeta(s). - R. J. Mathar, Feb 19 2011

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