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A014681 Fix 0; exchange even and odd numbers. 29
0, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
A self-inverse permutation of the nonnegative numbers.
If we ignore the first term 0, then this can be obtained as: a(n) is the smallest number different from n, not occurring earlier and coprime to n. - Amarnath Murthy, Apr 16 2003 [Corrected by Alois P. Heinz, May 06 2015]
a(0)=0, a(1)=2, then repeatedly subtract 1 and then add 3. - Jon Perry, Aug 12 2014
The biggest term of the pair [a(n), a(n+1)] is always even. This is the lexicographically first sequence with this property starting with a(1) = 0 and always extented with the smallest integer not yet present. - Eric Angelini, Feb 20 2017
LINKS
FORMULA
G.f.: x*(2-x+x^2)/((1-x)*(1-x^2)). - N. J. A. Sloane
a(n) = n - (-1)^n = a(n-1) + a(n-2) - a(n-3) = a(n-2) + 2. - Henry Bottomley, Mar 29 2000
a(0) = 0; a(2m+1) = 2m+2; for m > 0 a(2m) = 2m - 1. - George E. Antoniou, Dec 04 2001
a(n) = n - (-1)^n + 0^n for n >= 0. - Bruno Berselli, Nov 16 2010
E.g.f.: 1 + (x - 1)*cosh(x) + (1 + x)*sinh(x). - Stefano Spezia, Sep 02 2022
MATHEMATICA
Table[n - (-1)^n, {n, 1, 60}]
Join[{0}, LinearRecurrence[{1, 1, -1}, {2, 1, 4}, 69]] (* Ray Chandler, Sep 03 2015 *)
PROG
(PARI) a(n)=n - (-1)^n \\ Charles R Greathouse IV, May 06 2015
CROSSREFS
Composing this permutation with A065190 gives A065164.
Equals 1 + A004442.
Cf. A103889.
Sequence in context: A167542 A167419 A114285 * A103889 A137805 A163501
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)