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Search: id:A004442
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| A004442 |
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Natural numbers, pairs reversed: a(n) = n + (-1)^n; also Nimsum n + 1. |
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+0
23
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| 1, 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 18, 21, 20, 23, 22, 25, 24, 27, 26, 29, 28, 31, 30, 33, 32, 35, 34, 37, 36, 39, 38, 41, 40, 43, 42, 45, 44, 47, 46, 49, 48, 51, 50, 53, 52, 55, 54, 57, 56, 59, 58, 61, 60, 63, 62, 65, 64, 67, 66, 69
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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A self-inverse permutation of the natural numbers.
Nonnegative numbers rearranged with least disturbance to maintain a(n) not equal to n. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 13 2002
Essentially lodumo_2 of A059841 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 26 2009]
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REFERENCES
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E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 60.
J. H. Conway, On Numbers and Games. Academic Press, NY, 1976, pp. 51-53.
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LINKS
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Index entries for sequences related to Nim-sums
Index entries for sequences that are permutations of the natural numbers
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FORMULA
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a(n) = n XOR 1. - Odimar Fabeny (aifab(AT)yahoo.com.br), Sep 05 2004
G.f.: (1-x+2x^2)/((1-x)*(1-x^2)) - Mitchell Harris, Jan 10 2005
a(n+1)= lod_2(A059841(n)). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 26 2009]
a(n)=2*n-a(n-1)-3 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 21 2009]
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EXAMPLE
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For n=2, a(2)=2*2-1-3=0; n=3, a(3)=2*3-0-3=3; n=4, a(4)=2*4-3-3=2; [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 21 2009]
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MAPLE
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a[0]:=1:a[1]:=0:for n from 2 to 70 do a[n]:=a[n-2]+2 od: seq(a[n], n=0..68); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 19 2008
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MATHEMATICA
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Table[n + (-1)^n, {n, 0, 72}] (* or *)
CoefficientList[Series[(1 - x + 2x^2)/((1 - x)(1 - x^2)), {x, 0, 72}], x] (from Robert G. Wilson v (rgwv(at)rgwv.com), Jun 16 2006)
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CROSSREFS
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Cf. A003987, A004443, A004444. Equals A014681 - 1.
Sequence in context: A066250 A066251 A114882 this_sequence A065190 A152208 A085230
Adjacent sequences: A004439 A004440 A004441 this_sequence A004443 A004444 A004445
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KEYWORD
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nonn,easy,nice,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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