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A074066
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Zigzag modulo 3.
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5
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1, 4, 3, 2, 7, 6, 5, 10, 9, 8, 13, 12, 11, 16, 15, 14, 19, 18, 17, 22, 21, 20, 25, 24, 23, 28, 27, 26, 31, 30, 29, 34, 33, 32, 37, 36, 35, 40, 39, 38, 43, 42, 41, 46, 45, 44, 49, 48, 47, 52, 51, 50, 55, 54, 53, 58, 57, 56, 61, 60, 59, 64, 63, 62, 67, 66, 65, 70, 69
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(1)=1; for n>0: a(3*n-1)=3*n+1, a(3*n)=3*n, a(3*n+1)=3*n-1.
a(a(n))=n (self-inverse permutation); for n>1: a(n) = n iff n == 0 modulo 3.
Take natural numbers, exchange trisections starting with 2 and 4.
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LINKS
| 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
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FORMULA
| For n>1: a(n) = 3*floor(n/3) + (n mod 3)^2 * (-1)^(n mod 3); a(1)=1.
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MATHEMATICA
| a[n_] := n + Mod[n, 3]*(3*Mod[n, 3] - 5); a[1] = 1; Table[a[n], {n, 1, 69}] (* From Jean-François Alcover, Nov 04 2011 *)
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CROSSREFS
| Cf. A064429, A074067, A074068.
Sequence in context: A177037 A010651 A194758 * A067016 A022295 A132668
Adjacent sequences: A074063 A074064 A074065 * A074067 A074068 A074069
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KEYWORD
| nonn,nice
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 17 2002
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