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A093178
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If n is even then 1, otherwise n.
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23
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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
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OFFSET
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0,4
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COMMENTS
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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
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LINKS
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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
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FORMULA
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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
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EXAMPLE
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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 + ...
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MAPLE
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A093178:=n->(n+1+(1-n)*(-1)^n)/2; seq(A093178(k), k=0..100); # Wesley Ivan Hurt, Oct 19 2013
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MATHEMATICA
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Join[{1}, Riffle[Range[1, 85, 2], 1]] (* or *) Array[If[EvenQ[#], 1, #]&, 87, 0] (* Harvey P. Dale, Nov 23 2011 *)
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PROG
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(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
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CROSSREFS
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Equals |A009001(n)|.
Cf. A133080, A049471 (decimal expansion), A009001, A161738, A062557, A124625.
Sequence in context: A327531 A327514 A009001 * A307153 A300330 A328478
Adjacent sequences: A093175 A093176 A093177 * A093179 A093180 A093181
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KEYWORD
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nonn,easy
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AUTHOR
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Michael Somos, Mar 27 2004
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STATUS
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approved
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