A074068 Zigzag modulo 7.

1, 2, 3, 10, 9, 8, 7, 6, 5, 4, 17, 16, 15, 14, 13, 12, 11, 24, 23, 22, 21, 20, 19, 18, 31, 30, 29, 28, 27, 26, 25, 38, 37, 36, 35, 34, 33, 32, 45, 44, 43, 42, 41, 40, 39, 52, 51, 50, 49, 48, 47, 46, 59, 58, 57, 56, 55, 54, 53, 66, 65, 64, 63, 62, 61, 60, 73, 72, 71

Offset

1,2

Comments

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

for n>1: a(n) = n iff n == 0 modulo 7.

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

Formula

a(n) = 7*floor(n/7) + 14*floor((n mod 7)/4) - (n mod 7) for n>3; a(n)=n for n<=3.

a(n) = a(n-1) + a(n-7) - a(n-8) for n > 11. - Chai Wah Wu, May 25 2016

g.f.: x+2*x^2+3*x^3 + x^4*(10-x-x^2-x^3-x^4-x^5-x^6+3*x^7) / ( (x^6+x^5+x^4+x^3+x^2+x+1)*(x-1)^2 ). - R. J. Mathar, May 22 2019

Mathematica

Range[3]~Join~Flatten[Reverse /@ Partition[Range[4, 73], 7]] (* after Harvey P. Dale at A074066, or *)
Range[3]~Join~Table[7 Floor[n/7] + 14 Floor[#/4] - # &@ Mod[n, 7], {n, 4, 69}] (* Michael De Vlieger, May 25 2016 *)

Prog

(Haskell)
a074068 n = a074068_list !! (n-1)
a074068_list = 1 : 2 : 3 : xs where
   xs = 10 : 9 : 8 : 7 : 6 : 5 : 4 : map (+ 7) xs
-- Reinhard Zumkeller, Feb 21 2011

Crossrefs

Cf. A074066, A074067.

Sequence in context: A369991 A193729 A303115 * A351413 A283436 A225558

Adjacent sequences: A074065 A074066 A074067 * A074069 A074070 A074071

Keyword

nonn,look

Author

Reinhard Zumkeller, Aug 17 2002

Status

approved