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A074067 Zigzag modulo 5. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A333521 A333205 A011263 * A110988 A047224 A127817

Adjacent sequences: A074064 A074065 A074066 * A074068 A074069 A074070

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Aug 17 2002

STATUS

approved

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Last modified December 1 05:02 EST 2022. Contains 358454 sequences. (Running on oeis4.)