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

Author

Reinhard Zumkeller, Aug 17 2002

Keywords

• nonn
• easy
• look

Links

• Eric Weisstein's World of Mathematics, Alternating Permutations.
• Reinhard Zumkeller, Illustration for A074066-A074068.
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1).
• Index entries for sequences that are permutations of the natural numbers.

Crossrefs

Cf. A002162, A074066, A074067.

Programs

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

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 *)
LinearRecurrence[{1,0,0,0,0,0,1,-1},{1,2,3,10,9,8,7,6,5,4,17},80] (* Harvey P. Dale, Jan 19 2025 *)

Formula

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

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

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

Sum_{n>=1} (-1)^(n+1)/a(n) = log(2) (A002162). - Amiram Eldar, May 11 2025