A074067 Zigzag modulo 5.

1, 2, 7, 6, 5, 4, 3, 12, 11, 10, 9, 8, 17, 16, 15, 14, 13, 22, 21, 20, 19, 18, 27, 26, 25, 24, 23, 32, 31, 30, 29, 28, 37, 36, 35, 34, 33, 42, 41, 40, 39, 38, 47, 46, 45, 44, 43, 52, 51, 50, 49, 48, 57, 56, 55, 54, 53, 62, 61, 60, 59, 58, 67, 66, 65, 64, 63, 72, 71

Offset

1,2

Comments

a(a(n))=n (a self-inverse permutation);

for n>1: a(n) = n iff n == 0 modulo 5.

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 (1,0,0,0,1,-1)

Formula

a(n) = 5*floor(n/5) + 10*floor((n mod 5)/3) - (n mod 5) for n>2; a(n)=n for n<=2.

a(n) = a(n-1) + a(n-5) - a(n-6) for n > 8. - Chai Wah Wu, May 25 2016

g.f.: x+2*x + x^3*(7-x-x^2-x^3-x^4+2*x^5) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - R. J. Mathar, May 22 2019

Mathematica

{1, 2}~Join~Flatten[Reverse /@ Partition[Range[3, 72], 5]] (* after Harvey P. Dale at A074066, or *)
{1, 2}~Join~Table[5 Floor[n/5] + 10 Floor[#/3] - # &@ Mod[n, 5], {n, 3, 69}] (* Michael De Vlieger, May 25 2016 *)

Prog

(Haskell)
a074067 n = a074067_list !! (n-1)
a074067_list = 1 : 2 : xs where xs = 7 : 6 : 5 : 4 : 3 : map (+ 5) xs
-- Reinhard Zumkeller, Feb 21 2011

Crossrefs

Cf. A074066, A074068.

Sequence in context: A359533 A333205 A011263 * A110988 A047224 A127817

Adjacent sequences: A074064 A074065 A074066 * A074068 A074069 A074070

Keyword

nonn,easy

Author

Reinhard Zumkeller, Aug 17 2002

Status

approved