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

0,1

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).

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

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 *)

Prog

(Haskell)
a168184 = (1 -) . (0 ^) . (`mod` 10)
a168184_list = cycle [0, 1, 1, 1, 1, 1, 1, 1, 1, 1]
-- Reinhard Zumkeller, Oct 10 2012
(PARI) a(n)=n%10>0 \\ Charles R Greathouse IV, Sep 24 2015

Crossrefs

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

Sequence in context: A368905 A188642 A168046 * A013595 A339145 A368912

Adjacent sequences: A168181 A168182 A168183 * A168185 A168186 A168187

Keyword

nonn,easy

Author

Reinhard Zumkeller, Nov 30 2009

Status

approved