A074066 Zigzag modulo 3.

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

Offset

1,2

Comments

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

Index entries for sequences that are permutations of the natural numbers.

Formula

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.

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

Sum_{n>=1} (-1)^(n+1)/a(n) = log(2) (A002162). - Amiram Eldar, Dec 24 2023

Mathematica

a[n_] := n + Mod[n, 3]*(3*Mod[n, 3] - 5); a[1] = 1; Table[a[n], {n, 1, 69}] (* Jean-François 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. A002162, 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