A093178 If n is even then 1, otherwise n.

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

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 continued fractions for constants

Index entries for two-way infinite sequences

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

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)};

Crossrefs

Equals |A009001(n)|.

Cf. A133080, A049471 (decimal expansion), A009001, A161738, A062557, A124625.

Sequence in context: A327531 A327514 A009001 * A340086 A307153 A378513

Adjacent sequences: A093175 A093176 A093177 * A093179 A093180 A093181

Keyword

nonn,easy

Author

Michael Somos, Mar 27 2004

Status

approved