The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A000035 Period 2: repeat [0, 1]; a(n) = n mod 2; parity of n. (Formerly M0001) 594
 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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Least significant bit of n, lsb(n). Also decimal expansion of 1/99. Also the binary expansion of 1/3. - Robert G. Wilson v, Sep 01 2015 a(n) = A134451(n) mod 2. - Reinhard Zumkeller, Oct 27 2007 [Corrected by Jianing Song, Nov 22 2019] Characteristic function of odd numbers: a(A005408(n)) = 1, a(A005843(n)) = 0. - Reinhard Zumkeller, Sep 29 2008 A102370(n) modulo 2. - Philippe Deléham, Apr 04 2009 Base b expansion of 1/(b^2-1) for any b >= 2 is 0.0101... (A005563 has b^2-1). - Rick L. Shepherd, Sep 27 2009 Let A be the Hessenberg n X n matrix defined by: A[1,j] = j mod 2, A[i,i] := 1, A[i,i-1] = -1, and A[i,j] = 0 otherwise. Then, for n >= 1, a(n) = (-1)^n*charpoly(A,1). - Milan Janjic, Jan 24 2010 From R. J. Mathar, Jul 15 2010: (Start) The sequence is the principal Dirichlet character of the reduced residue system mod 2 or mod 4 or mod 8 or mod 16 ... Associated Dirichlet L-functions are for example L(2,chi) = Sum_{n>=1} a(n)/n^2 == A111003, or L(3,chi) = Sum_{n>=1} a(n)/n^3 = 1.05179979... = 7*A002117/8, or L(4,chi) = Sum_{n>=1} a(n)/n^4 = 1.014678... = A092425/96. (End) Also parity of the nonnegative integers A001477. - Omar E. Pol, Jan 17 2012 a(n) = (4/n), where (k/n) is the Kronecker symbol. See the Eric Weisstein link. - Wolfdieter Lang, May 28 2013 Also the inverse binomial transform of A131577. - Paul Curtz, Nov 16 2016 [an observation forwarded by Jean-François Alcover] The emanation sequence for the globe category. That is take the globe category, take the corresponding polynomial comonad, consider its carrier polynomial as a generating function, and take the corresponding sequence. - David Spivak, Sep 25 2020 For n > 0, a(n) is the alternating sum of the product of n increasing and n decreasing odd factors. For example, a(4) = 1*7 - 3*5 + 5*3 - 7*1 and a(5) = 1*9 - 3*7 + 5*5 - 7*3 + 9*1. - Charlie Marion, Mar 24 2022 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS David Wasserman, Table of n, a(n) for n = 0..1000 Paul Barry, A Catalan Transform and Related Transformations on Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5. F. Javier de Vega, An extension of Furstenberg's theorem of the infinitude of primes, arXiv:2003.13378 [math.NT], 2020. Clark Kimberling, A Combinatorial Classification of Triangle Centers on the Line at Infinity, J. Int. Seq., Vol. 22 (2019), Article 19.5.4. Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1. Eric Weisstein's World of Mathematics, Dirichlet Series Generating Function Eric Weisstein's World of Mathematics, Kronecker Symbol A. K. Whitford, Binet's Formula Generalized, Fibonacci Quarterly, Vol. 15, No. 1, 1979, pp. 21, 24, 29 Index entries for linear recurrences with constant coefficients, signature (0,1). FORMULA a(n) = (1 - (-1)^n)/2. a(n) = n mod 2. a(n) = 1 - a(n-1). Multiplicative with a(p^e) = p mod 2. - David W. Wilson, Aug 01 2001 G.f.: x/(1-x^2). E.g.f.: sinh(x). - Paul Barry, Mar 11 2003 a(n) = (A000051(n) - A014551(n))/2. - Mario Catalani (mario.catalani(AT)unito.it), Aug 30 2003 a(n) = ceiling((-2)^(-n-1)). - Reinhard Zumkeller, Apr 19 2005 a(n) = (sin(n*Pi/2))^2 = (cos(n*Pi/2 +- Pi/2))^2 for n >= 0. - Paolo P. Lava, Sep 20 2006 Dirichlet g.f.: (1-1/2^s)*zeta(s). - R. J. Mathar, Mar 04 2011 a(n) = ceiling(n/2) - floor(n/2). - Arkadiusz Wesolowski, Sep 16 2012 a(n) = ceiling( cos(Pi*(n-1))/2 ). - Wesley Ivan Hurt, Jun 16 2013 a(n) = floor((n-1)/2) - floor((n-2)/2). - Mikael Aaltonen, Feb 26 2015 Dirichlet g.f.: L(chi(2),s) with chi(2) the principal Dirichlet character modulo 2. - Ralf Stephan, Mar 27 2015 a(n) = 0^^n = 0^(0^(0...)) (n times), where we take 0^0 to be 1. - Natan Arie Consigli, May 02 2015 MAPLE A000035 := n->n mod 2; [ seq(i mod 2, i=0..100) ]; MATHEMATICA PadLeft[{}, 110, {0, 1}] (* Harvey P. Dale, Sep 25 2011 *) PROG (PARI) a(n)=n%2; (PARI) a(n)=direuler(p=1, 100, if(p==2, 1, 1/(1-X)))[n] /* Ralf Stephan, Mar 27 2015 */ (Haskell) a000035 n = n `mod` 2  -- James Spahlinger, Oct 08 2012 (Haskell) a000035_list = cycle [0, 1]  -- Reinhard Zumkeller, Jan 06 2012 (Maxima) A000035(n):=mod(n, 2)\$ makelist(A000035(n), n, 0, 30); /* Martin Ettl, Nov 12 2012 */ (Scheme) (define (A000035 n) (mod n 2)) ;; For R6RS. Use modulo in older Schemes like MIT/GNU Scheme. - Antti Karttunen, Mar 21 2017 (Python) def A000035(n): return n & 1 # Chai Wah Wu, May 25 2022 CROSSREFS Ones complement of A059841. Cf. A053644 for most significant bit. This is Guy Steele's sequence GS(1, 2) (see A135416). Period k zigzag sequences: this sequence (k=2), A007877 (k=4), A260686 (k=6), A266313 (k=8), A271751 (k=10), A271832 (k=12), A279313 (k=14), A279319 (k=16), A158289 (k=18). Cf. A154955 (Mobius transform). Sequence in context: A173923 A260393 A125122 * A188510 A131734 A134452 Adjacent sequences:  A000032 A000033 A000034 * A000036 A000037 A000038 KEYWORD cons,core,easy,nonn,nice,mult AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 1 11:09 EDT 2022. Contains 354972 sequences. (Running on oeis4.)