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 A093178 If n is even then 1, otherwise n. 24
 1, 1, 1, 3, 1, 5, 1, 7, 1, 9, 1, 11, 1, 13, 1, 15, 1, 17, 1, 19, 1, 21, 1, 23, 1, 25, 1, 27, 1, 29, 1, 31, 1, 33, 1, 35, 1, 37, 1, 39, 1, 41, 1, 43, 1, 45, 1, 47, 1, 49, 1, 51, 1, 53, 1, 55, 1, 57, 1, 59, 1, 61, 1, 63, 1, 65, 1, 67, 1, 69, 1, 71, 1, 73, 1, 75, 1, 77, 1, 79, 1, 81, 1, 83, 1, 85 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Continued fraction expansion for tan(1). 1 followed by run lengths of A062557 = 2n-1 1's followed by a 2. - Jeremy Gardiner, Aug 12 2012 Greatest common divisor of n and (n+1) mod 2. - Bruno Berselli, Mar 07 2017 LINKS Harry J. Smith, Table of n, a(n) for n = 0..20000 D. H. Lehmer, Continued fractions containing arithmetic progressions, Scripta Mathematica, 29 (1973): 17-24. [Annotated copy of offprint] Simon Plouffe, A Search for a mathematical expression for mass ratios using a large database. page 3. G. Xiao, Contfrac Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1). FORMULA G.f.: (1+x-x^2+x^3)/(1-x^2)^2. a(n) = (-1)^n * a(-n) for all n in Z. a(n) = (1/2) * [ 1 + n + (1-n)*(-1)^n ]. - Ralf Stephan, Dec 02 2004 a(n) = n^n mod (n+1) for n > 0. - Amarnath Murthy, Apr 18 2004 Satisfies a(0) = 1, a(n+1) = a(n) + n if a(n) < n else a(n+1) = a(n)/n. - Amarnath Murthy, Oct 29 2002 a(n) = ((n+1)+(1-n)(-1)^n)/2 and have e.g.f. (1+x)cosh(x). - Paul Barry, Apr 09 2003 a(n) = binomial(n, 2*floor(n/2)). - Paul Barry, Dec 28 2006 a(n) = binomial(n, (n mod 2)). - Paolo P. Lava, Aug 29 2007 Starting (1, 1, 3, 1, 5, 1, 7,...) = A133080^(-1) * [1,2,3,...]. - Gary W. Adamson, Sep 08 2007 a(n) = denom(b(n+2)/b(n+1)) with b(n) = product((2*n-3-2*k), k=0..floor(n/2-1)). - Johannes W. Meijer, Jun 18 2009 a(n) = 2*floor(n/2) - n*(n-1 mod 2) + 1. - Wesley Ivan Hurt, Oct 19 2013 a(n) = n^(n mod 2). - Wesley Ivan Hurt, Apr 16 2014 EXAMPLE 1.557407724654902230506974807... = 1 + 1/(1 + 1/(1 + 1/(3 + 1/(1 + ...)))) G.f. = 1 + x + x^2 + 3*x^3 + x^4 + 5*x^5 + x^6 + 7*x^7 + x^8 + 9*x^9 + x^10 + ... MAPLE A093178:=n->(n+1+(1-n)*(-1)^n)/2; seq(A093178(k), k=0..100); # Wesley Ivan Hurt, Oct 19 2013 MATHEMATICA Join[{1}, Riffle[Range[1, 85, 2], 1]] (* or *) Array[If[EvenQ[#], 1, #]&, 87, 0] (* Harvey P. Dale, Nov 23 2011 *) PROG (PARI) {a(n) = if( n%2, n, 1)}; (PARI) { allocatemem(932245000); default(realprecision, 79000); x=contfrac(tan(1)); for (n=0, 20000, write("b093178.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 13 2009 CROSSREFS Equals |A009001(n)|. Cf. A133080, A049471 (decimal expansion), A009001, A161738, A062557, A124625. Sequence in context: A327531 A327514 A009001 * A340086 A307153 A339421 Adjacent sequences:  A093175 A093176 A093177 * A093179 A093180 A093181 KEYWORD nonn,easy AUTHOR Michael Somos, Mar 27 2004 STATUS approved

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Last modified April 21 04:42 EDT 2021. Contains 343146 sequences. (Running on oeis4.)