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A080782
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a(1)=1, a(n)=a(n-1)-1 if n is already in the sequence, a(n)=a(n-1)+2 otherwise.
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8
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1, 3, 2, 4, 6, 5, 7, 9, 8, 10, 12, 11, 13, 15, 14, 16, 18, 17, 19, 21, 20, 22, 24, 23, 25, 27, 26, 28, 30, 29, 31, 33, 32, 34, 36, 35, 37, 39, 38, 40, 42, 41, 43, 45, 44, 46, 48, 47, 49, 51, 50, 52, 54, 53, 55, 57, 56, 58, 60, 59, 61, 63, 62, 64, 66, 65, 67, 69, 68
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OFFSET
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1,2
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COMMENTS
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Permutation of the integers: exchange trisections starting with 2 and 3.
a(a(n)) = n. - Reinhard Zumkeller, Oct 29 2004
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LINKS
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Guenther Schrack, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
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FORMULA
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a(n) - n is periodic with period 3.
a(n) = n + ((n+1) mod 3), with n >= 0. - Paolo P. Lava, Jun 26 2007
G.f.: x*(1+2*x-x^2+x^3)/(1-x-x^3+x^4). - Jaume Oliver Lafont, Mar 24 2009
a(0)=1, a(1)=3, a(2)=2, a(3)=4, a(n)=a(n-1)+0*a(n-2)+a(n-3)-a(n-4). - Harvey P. Dale, Mar 29 2013
a(n) = n + (2/sqrt(3))*sin(2*(n+2)*Pi/3). - Wesley Ivan Hurt, Sep 26 2017
From Guenther Schrack, Oct 23 2019: (Start)
a(n) = a(n-3) + 3 with a(1) = 1, a(2) = 3, a(3) = 2 for n > 3.
a(n) = n - (w^(2*n)*(2 + w) + w^n*(1 - w))/3 where w = (-1 + sqrt(-3))/2. (End)
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MATHEMATICA
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Array[#+Mod[#+1, 3]&, 70, 0] (* or *) LinearRecurrence[{1, 0, 1, -1}, {1, 3, 2, 4}, 70] (* Harvey P. Dale, Mar 29 2013 *)
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CROSSREFS
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Cf. A079357, A079354, A080783, A064437.
Equals A064429(n-1) + 1. Cf. A004442, A080412.
Sequence in context: A187566 A049831 A186005 * A116941 A166695 A254107
Adjacent sequences: A080779 A080780 A080781 * A080783 A080784 A080785
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KEYWORD
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nonn,easy
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AUTHOR
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Benoit Cloitre, Mar 07 2003
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STATUS
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approved
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