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 A103889 Odd and even positive integers swapped. 30
 2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31, 34, 33, 36, 35, 38, 37, 40, 39, 42, 41, 44, 43, 46, 45, 48, 47, 50, 49, 52, 51, 54, 53, 56, 55, 58, 57, 60, 59, 62, 61, 64, 63, 66, 65, 68, 67, 70, 69, 72, 71 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS (a(n)-1)*(a(n-1)+1) = 2*A176222(n+1) for n>1; (a(n)-1)*(a(n-3)+1) = 2*A176222(n) for n>3. - Bruno Berselli, Nov 16 2010 For n >= 5, also the number of (undirected) Hamiltonian cycles in the (n-2)-Moebius ladder. - Eric W. Weisstein, May 06 2019 For n >= 4, also the number of (undirected) Hamiltonian cycles in the (n-1)-prism graph. - Eric W. Weisstein, May 06 2019 The lexicographically first involution of the natural numbers with no fixed points. - Alexander Fraebel, Sep 08 2020 LINKS Eric Weisstein's World of Mathematics, Hamiltonian Cycle Eric Weisstein's World of Mathematics, Moebius Ladder Eric Weisstein's World of Mathematics, Prism Graph Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA a(2k) = 2k-1 = A005408(k), a(2k-1) = 2k = A005843(k), k=1, 2, ... O.g.f.: x*(x^2-x+2)/[(x-1)^2*(1+x)]. - R. J. Mathar, Apr 06 2008 a(n) = n-1+2*(n mod 2). - Rolf Pleisch, Apr 22 2008 a(n) = 2*n-a(n-1)-1 (with a(1)=2). - Vincenzo Librandi, Nov 16 2010 a(n) = n-(-1)^n. a(n)-a(n-1)-a(n-2)+a(n-3) = 0 for n>3. - Bruno Berselli, Nov 16 2010 MATHEMATICA Table[{n + 1, n}, {n, 1, 100, 2}] // Flatten Table[n - (-1)^n, {n, 25}] (* Eric W. Weisstein, May 06 2019 *) PROG [ n eq 1 select 2 else -Self(n-1)+2*n-1: n in [1..72] ]; (Haskell) import Data.List (transpose) a103889 n = n - 1 + 2 * mod n 2 a103889_list = concat \$ transpose [tail a005843_list, a005408_list] -- Reinhard Zumkeller, Jun 23 2013, Feb 21 2011 (PARI) a(n)=n-1+if(n%2, 2) \\ Charles R Greathouse IV, Feb 24 2011 CROSSREFS Essentially the same as A014681. Odd numbers: A005408. Even numbers: A005843. Cf. A103889, A004442. Sequence in context: A167419 A114285 A014681 * A137805 A163501 A306229 Adjacent sequences:  A103886 A103887 A103888 * A103890 A103891 A103892 KEYWORD nonn,easy AUTHOR Zak Seidov, Feb 20 2005 STATUS approved

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Last modified June 24 18:46 EDT 2021. Contains 345419 sequences. (Running on oeis4.)