OFFSET
0,1
COMMENTS
a(n) is 0 if 6 divides n, 1 otherwise.
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..26244
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).
FORMULA
G.f.: 1/(1-x) - 1/(1-x^6) = Sum_{k>=0} x^k - x^(6*k).
Recurrence: a(n+6) = a(n), a(0) = 0, a(i) = 1, 1 <= i <= 5.
a(n) = (1/4) * (3 - (-1)^n - (-1)^((n+1)/3) - (-1)^((2n+1)/3)).
From Reinhard Zumkeller, Nov 30 2009: (Start)
a(n) = 1 - A079979(n).
A033438(n) = Sum_{k=0..n} a(k)*(n-k). (End)
Dirichlet g.f.: (1 - 1/6^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
a(n) = sign(n mod 6). - Wesley Ivan Hurt, Jun 29 2013
a(n) = ceiling(5n/6) - floor(5n/6). - Wesley Ivan Hurt, Jun 20 2014
MAPLE
seq(signum(k mod 6), k=0..100); # Wesley Ivan Hurt, Jun 29 2013
MATHEMATICA
Table[Boole[Not[Divisible[n, 6]]], {n, 0, 89}] (* Alonso del Arte, Oct 21 2013 *)
PadRight[{}, 120, {0, 1, 1, 1, 1, 1}] (* Michael De Vlieger, Dec 22 2017 *)
PROG
(PARI) a(n) = sign(n%6);
(Magma) [Sign(n mod 6) : n in [0..50]]; // Wesley Ivan Hurt, Jun 20 2014
(Scheme) (define (A097325 n) (if (zero? (modulo n 6)) 0 1)) ;; Antti Karttunen, Dec 22 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ralf Stephan, Aug 16 2004
EXTENSIONS
New name from Omar E. Pol, Oct 21 2013
STATUS
approved