

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
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OFFSET

1,2


COMMENTS

a(a(n))=n (a selfinverse 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 A074066A074068
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(n1) + a(n5)  a(n6) for n > 8.  Chai Wah Wu, May 25 2016
g.f.: x+2*x + x^3*(7xx^2x^3x^4+2*x^5) / ( (x^4+x^3+x^2+x+1)*(x1)^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 !! (n1)
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



