|
| |
|
|
A168181
|
|
Characteristic function of numbers that are not multiples of 8.
|
|
15
|
|
|
|
0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,1
|
|
|
COMMENTS
|
Multiplicative with a(p^e) = (if p=2 then A019590(e) else 1), p prime and e>0.
Period 8 Repeat: [0, 1, 1, 1, 1, 1, 1, 1]. - Wesley Ivan Hurt, Jun 21 2014
|
|
|
LINKS
|
Table of n, a(n) for n=0..104.
Index entries for characteristic functions
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1).
|
|
|
FORMULA
|
a(n+8) = a(n);
a(n) = A000007(A010877(n));
a(A047592(n)) = 1; a(A008590(n)) = 0;
A033440(n) = SUM(a(k)*(n-k): 0<=k<=n).
Dirichlet g.f. (1-1/8^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 8). - Wesley Ivan Hurt, Jun 21 2014
a(n) = sign( 1 - floor(cos(Pi*n/4)) ). - Wesley Ivan Hurt, Jun 21 2014
Euler transform of length 8 sequence [ 1, 0, 0, 0, 0, 0, -1, 1]. - Michael Somos, Jun 24 2014
Moebius transform is length 8 sequence [ 1, 0, 0, 0, 0, 0, 0, -1]. - Michael Somos, Jun 24 2014
G.f.: x * (1 - x^7) / ((1 - x) * (1 - x^8)). - Michael Somos, Jun 24 2014
|
|
|
EXAMPLE
|
G.f. = x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^9 + x^10 + x^11 + ...
|
|
|
MAPLE
|
with(numtheory); A168181:=n->signum(n mod 8); seq(A168181(n), n=0..100); # Wesley Ivan Hurt, Jun 21 2014
|
|
|
MATHEMATICA
|
Table[Sign[Mod[n, 8]], {n, 0, 100}] (* Wesley Ivan Hurt, Jun 21 2014 *)
|
|
|
PROG
|
(MAGMA) [Sign(n mod 8) : n in [0..100]]; // Wesley Ivan Hurt, Jun 21 2014
(PARI) a(n)=n%8 > 0 \\ Felix Fröhlich, Aug 11 2014
|
|
|
CROSSREFS
|
Cf. A168185, A145568, A168184, A168182, A109720, A097325, A011558, A166486, A011655, A000035.
Sequence in context: A109720 A022932 A079421 * A164980 A168182 A168046
Adjacent sequences: A168178 A168179 A168180 * A168182 A168183 A168184
|
|
|
KEYWORD
|
mult,nonn,easy
|
|
|
AUTHOR
|
Reinhard Zumkeller, Nov 30 2009
|
|
|
STATUS
|
approved
|
| |
|
|
