Search: id:A000035
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%I A000035 M0001
%S A000035 0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,
%T A000035 1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,
%U A000035 0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0
%N A000035 A simple periodic sequence.
%C A000035 Least significant bit of n, lsb(n).
%C A000035 Also decimal expansion of 1/99.
%C A000035 a(n) = ABS(A134451(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Oct 27 2007
%C A000035 Characteristic function of odd numbers: a(A005408(n))=1, a(A005843(n))=0. 
               [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 29 
               2008]
%C A000035 A102370(n) modulo 2 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Apr 04 2009]
%C A000035 Base b expansion of 1/(b^2-1) for any b>=2 is 0.0101... (A005563 has 
               b^2-1). [From Rick L. Shepherd (rshepherd2(AT)hotmail.com), Sep 27 
               2009]
%D A000035 Paul Barry, A Catalan Transform and Related Transformations on Integer 
               Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.
%D A000035 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000035 A. K. Whitford, Binet's Formula Generalized, Fib. Quart., 15 (1977), 
               pp. 21, 24, 29.
%H A000035 David Wasserman, <a href="b000035.txt">Table of n, a(n) for n = 0..1000</
               a>
%H A000035 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A000035 <a href="Sindx_Ch.html#char_fns">Index entries for characteristic functions</
               a>
%H A000035 Y. Puri and T. Ward, <a href="http://www.cs.uwaterloo.ca/journals/JIS/
               index.html">Arithmetic and growth of periodic orbits</a>, J. Integer 
               Seqs., Vol. 4 (2001), #01.2.1.
%H A000035 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DirichletSeriesGeneratingFunction.html">Dirichlet Series Generating 
               Function</a>
%H A000035 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               KroneckerSymbol.html">Kronecker Symbol</a>
%H A000035 <a href="Sindx_Cor.html#core">Index entries for "core" sequences</a>
%F A000035 a(n)={1 - (-1)^n}/2. a(n) = n mod 2.
%F A000035 Multiplicative with a(p^e) = p%2. - David W. Wilson (davidwwilson(AT)comcast.net), 
               Aug 01, 2001.
%F A000035 G.f.: x/(1-x^2). E.g.f.: sinh(x). a(n)=n mod 2. a(n)=1/2 - (-1)^n/2. 
               - Paul Barry (pbarry(AT)wit.ie), Mar 11 2003
%F A000035 a(n)=(A000051(n)-A014551(n))/2. - Mario Catalani (mario.catalani(AT)unito.it), 
               Aug 30 2003
%F A000035 a(n) = ceiling((-2)^(-n-1)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Apr 19 2005
%F A000035 a(n)= [sin(n*Pi/2)]^2 = [cos(n*Pi/2 +/- Pi/2)]^2 with n>=0. - Paolo P. 
               Lava (ppl(AT)spl.at), Sep 20 2006
%p A000035 A000035 := n->n mod 2;
%p A000035 [ seq(i mod 2, i=0..100) ];
%t A000035 Nest[Flatten[ # /. {0 -> {0, 1}, 1 -> {0, 1}}] &, {0}, 7] (from Robert 
               G. Wilson v Mar 05 2005)
%t A000035 Nest[ Flatten[ # /. {0 -> {0, 1, 0}}] &, {0}, 5] (* Robert G. Wilson 
               v Sep 01 2005 *)
%t A000035 CellularAutomaton[50, {{0, 1}, 0}, 104, {All, {0}}] // Flatten [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2009]
%o A000035 (PARI) a(n)=n%2
%o A000035 See link in A140080 for Fortran program.
%Y A000035 Ones complement of A059841. Cf. A053644 for most significant bit.
%Y A000035 This is Guy Steele's sequence GS(1, 2) (see A135416).
%Y A000035 Sequence in context: A112416 A061265 A125122 this_sequence A131734 A134452 
               A071029
%Y A000035 Adjacent sequences: A000032 A000033 A000034 this_sequence A000036 A000037 
               A000038
%K A000035 core,easy,nonn,nice,mult
%O A000035 0,1
%A A000035 N. J. A. Sloane (njas(AT)research.att.com).

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