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 A168181 Characteristic function of numbers that are not multiples of 8. 16
 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 Antti Karttunen, Table of n, a(n) for n = 0..16384 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_{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 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 (Python) def A168181(n): return int(bool(n&7)) # Chai Wah Wu, Jul 09 2022 CROSSREFS 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 KEYWORD mult,nonn,easy AUTHOR Reinhard Zumkeller, Nov 30 2009 STATUS approved

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Last modified December 7 21:25 EST 2022. Contains 358669 sequences. (Running on oeis4.)