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A168181
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Characteristic function of numbers that are not multiples of 8.
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16
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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
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OFFSET
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0,1
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COMMENTS
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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
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 0..16384
Index entries for characteristic functions
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1).
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FORMULA
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a(n+8) = a(n);
a(n) = A000007(A010877(n));
a(A047592(n)) = 1; a(A008590(n)) = 0;
A033440(n) = Sum_{k=0..n} a(k)*(n-k).
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
a(n) = 1-A253513(n). - Antti Karttunen, Oct 08 2017
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EXAMPLE
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G.f. = x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^9 + x^10 + x^11 + ...
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MAPLE
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with(numtheory); A168181:=n->signum(n mod 8); seq(A168181(n), n=0..100); # Wesley Ivan Hurt, Jun 21 2014
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MATHEMATICA
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Table[Sign[Mod[n, 8]], {n, 0, 100}] (* Wesley Ivan Hurt, Jun 21 2014 *)
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PROG
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(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
(Python)
def A168181(n): return int(bool(n&7)) # Chai Wah Wu, Jul 09 2022
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CROSSREFS
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Cf. A168185, A145568, A168184, A168182, A109720, A097325, A011558, A166486, A011655, A000035, A010877, A244413, A253513.
Sequence in context: A334812 A079421 A304438 * A324732 A164980 A252372
Adjacent sequences: A168178 A168179 A168180 * A168182 A168183 A168184
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KEYWORD
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mult,nonn,easy
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AUTHOR
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Reinhard Zumkeller, Nov 30 2009
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STATUS
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approved
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