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A074066 Zigzag modulo 3. 5
1, 4, 3, 2, 7, 6, 5, 10, 9, 8, 13, 12, 11, 16, 15, 14, 19, 18, 17, 22, 21, 20, 25, 24, 23, 28, 27, 26, 31, 30, 29, 34, 33, 32, 37, 36, 35, 40, 39, 38, 43, 42, 41, 46, 45, 44, 49, 48, 47, 52, 51, 50, 55, 54, 53, 58, 57, 56, 61, 60, 59, 64, 63, 62, 67, 66, 65, 70, 69 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(1)=1; for n>0: a(3*n-1) = 3*n+1, a(3*n) = 3*n, a(3*n+1) = 3*n-1.

a(a(n))=n (self-inverse permutation); for n>1: a(n) = n iff n == 0 modulo 3.

Take natural numbers, exchange trisections starting with 2 and 4.

LINKS

Table of n, a(n) for n=1..69.

Eric Weisstein's World of Mathematics, Alternating Permutations

Reinhard Zumkeller, Illustration for A074066-A074068

Index entries for sequences that are permutations of the natural numbers

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

FORMULA

For n > 1: a(n) = 3*floor(n/3) + (n mod 3)^2 * (-1)^(n mod 3); a(1)=1.

a(n) = a(n-1) + a(n-3) - a(n-4) for n > 5. - Chai Wah Wu, May 25 2016

For n > 1, a(n) = n - (4/sqrt(3))*sin(2*n*Pi/3). - Wesley Ivan Hurt, Sep 29 2017

g.f.: x + x^2*(4-x-x^2+x^3) / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, May 22 2019

MATHEMATICA

a[n_] := n + Mod[n, 3]*(3*Mod[n, 3] - 5); a[1] = 1; Table[a[n], {n, 1, 69}] (* Jean-Fran├žois Alcover, Nov 04 2011 *)

Join[{1}, Flatten[Reverse/@Partition[Range[2, 73], 3]]] (* Harvey P. Dale, Feb 17 2012 *)

PROG

(Haskell)

a074066 n = a074066_list !! (n-1)

a074066_list = 1 : xs where xs = 4 : 3 : 2 : map (+ 3) xs

-- Reinhard Zumkeller, Feb 21 2011

CROSSREFS

Cf. A064429, A074067, A074068.

Sequence in context: A010651 A286388 A194758 * A307648 A067016 A022295

Adjacent sequences:  A074063 A074064 A074065 * A074067 A074068 A074069

KEYWORD

nonn,easy,nice

AUTHOR

Reinhard Zumkeller, Aug 17 2002

STATUS

approved

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Last modified October 22 17:34 EDT 2019. Contains 328319 sequences. (Running on oeis4.)