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A103889
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Odd and even positive integers swapped.
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20
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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
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OFFSET
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1,1
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COMMENTS
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(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]
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LINKS
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Table of n, a(n) for n=1..72.
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
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FORMULA
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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]
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MATHEMATICA
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Table[{n + 1, n}, {n, 1, 100, 2}] // Flatten
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PROG
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[ 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
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CROSSREFS
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Essentially the same as A014681.
Odd numbers: A005408. Even numbers: A005843.
Cf. A103889, A004442.
Sequence in context: A167419 A114285 A014681 * A137805 A163501 A096779
Adjacent sequences: A103886 A103887 A103888 * A103890 A103891 A103892
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KEYWORD
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nonn,easy
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AUTHOR
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Zak Seidov, Feb 20 2005
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STATUS
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approved
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