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A121216
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a(1)=1, a(2) = 2; thereafter a(n) = the smallest positive integer which does not occur earlier in the sequence and which is coprime to a(n-2).
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24
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1, 2, 3, 5, 4, 6, 7, 11, 8, 9, 13, 10, 12, 17, 19, 14, 15, 23, 16, 18, 21, 25, 20, 22, 27, 29, 26, 24, 31, 35, 28, 32, 33, 37, 34, 30, 39, 41, 38, 36, 43, 47, 40, 42, 49, 53, 44, 45, 51, 46, 50, 55, 57, 48, 52, 59, 61, 54, 56, 65, 67, 58, 60, 63, 71, 62, 64, 69, 73, 68, 66, 75
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OFFSET
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1,2
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COMMENTS
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I confirm that this is a permutation. - N. J. A. Sloane, Mar 28 2015 [This can be proved using an argument similar to (but simpler than) the proof in A093714. - N. J. A. Sloane, May 05 2022]
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LINKS
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MATHEMATICA
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Nest[Append[#, Block[{k = 3}, While[Nand[FreeQ[#, k], GCD[#[[-2]], k] == 1], k++]; k]] &, {1, 2}, 70] (* Michael De Vlieger, Dec 26 2019 *)
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PROG
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(Haskell)
import Data.List (delete, (\\))
a121216 n = a121216_list !! (n-1)
a121216_list = 1 : 2 : f 1 2 [3..] where
f x y zs = g zs where
g (u:us) = if gcd x u == 1 then h $ delete u zs else g us where
h (v:vs) = if gcd y v == 1 then u : v : f u v (zs \\ [u, v]) else h vs
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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