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A064429
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a(n) = floor(n / 3) * 3 + sign(n mod 3) * (3 - n mod 3).
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10
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0, 2, 1, 3, 5, 4, 6, 8, 7, 9, 11, 10, 12, 14, 13, 15, 17, 16, 18, 20, 19, 21, 23, 22, 24, 26, 25, 27, 29, 28, 30, 32, 31, 33, 35, 34, 36, 38, 37, 39, 41, 40, 42, 44, 43, 45, 47, 46, 48, 50, 49, 51, 53, 52, 54, 56, 55, 57, 59, 58, 60, 62, 61, 63, 65, 64, 66, 68, 67, 69, 71, 70
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OFFSET
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0,2
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COMMENTS
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a(a(n)) = n (a self-inverse permutation).
Take natural numbers, exchange trisections starting with 1 and 2.
a(n) is also obtained as follows: write n in base 3; if the rightmost digit is '1', then replace it with '2' and vice versa; convert back to decimal. For example a(14) = a('11'2') = '11'1' = 13 and a(10) = a('10'1') = '10'2' = 11. (End)
A permutation of the nonnegative integers partitioned into triples [3*k-3, 3*k-1, 3*k-2] for k > 0. - Guenther Schrack, Feb 05 2020
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LINKS
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FORMULA
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G.f.: x*(2 - x + 2*x^2)/((1 + x + x^2)*(1 - x)^2 ). - R. J. Mathar, Feb 20 2011
a(n) = a(n-3) + 3 with a(0)=0, a(1)=2, a(2)=1 for n > 2;
a(n) = n + (w^(2*n) - w^n)*(1 + 2*w)/3 where w = (-1 + sqrt(-3))/2. (End)
Sum_{n>=1} (-1)^n/a(n) = log(2)/3. - Amiram Eldar, Jan 31 2023
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EXAMPLE
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Interleave 3 sequences:
A008585: 0.....3.....6.....9.......12.......15........
A016789: ..2.....5.....8.....11.......14.......17.....
A016777: ....1.....4.....7......10.......13.......16..
(End)
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MAPLE
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MATHEMATICA
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Table[2 n - 3 - 3 Floor[(n - 2)/3], {n, 0, 100}] (* Wesley Ivan Hurt, Nov 30 2013 *)
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PROG
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(PARI) a(n) = 2*n-3-3*((n-2)\3); \\ Altug Alkan, Oct 06 2017
(GAP) a:=[0, 2, 1, 3];; for n in [5..100] do a[n]:=a[n-1]+a[n-3]-a[n-4]; od; a; # Muniru A Asiru, Jul 27 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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