

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
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OFFSET

1,2


COMMENTS

a(1)=1; for n>0: a(3*n1) = 3*n+1, a(3*n) = 3*n, a(3*n+1) = 3*n1.
a(a(n))=n (selfinverse 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 A074066A074068
Index entries for sequences that are permutations of the natural numbers


FORMULA

For n > 1: a(n) = 3*floor(n/3) + (n mod 3)^2 * (1)^(n mod 3); a(1)=1.
a(n) = a(n1) + a(n3)  a(n4) 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


MATHEMATICA

a[n_] := n + Mod[n, 3]*(3*Mod[n, 3]  5); a[1] = 1; Table[a[n], {n, 1, 69}] (* JeanFrançois 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 !! (n1)
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 * A067016 A022295 A258415
Adjacent sequences: A074063 A074064 A074065 * A074067 A074068 A074069


KEYWORD

nonn,nice


AUTHOR

Reinhard Zumkeller, Aug 17 2002


STATUS

approved



