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A130508
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a(1)=2. a(2)=3. a(3)=1. a(n+3) = 3 + a(n), for all positive integers n.
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2
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2, 3, 1, 5, 6, 4, 8, 9, 7, 11, 12, 10, 14, 15, 13, 17, 18, 16, 20, 21, 19, 23, 24, 22, 26, 27, 25, 29, 30, 28, 32, 33, 31, 35, 36, 34, 38, 39, 37, 41, 42, 40, 44, 45, 43, 47, 48, 46, 50, 51, 49, 53, 54, 52, 56, 57, 55, 59, 60, 58, 62, 63, 61, 65, 66, 64, 68
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OFFSET
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1,1
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COMMENTS
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This sequence is a permutation of the positive integers, where each a(n) is the smallest positive integer not occurring earlier in the sequence such that the m-th term of the inverse permutation A130509 never equals a(m), for all positive integers m.
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LINKS
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FORMULA
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a(1)=2, a(2)=3, a(3)=1, a(4)=5, a(n)=a(n-1)+a(n-3)-a(n-4). - Harvey P. Dale, Feb 02 2015
G.f.: x*(2+x-2*x^2+2*x^3) / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 03 2021
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*Pi/(3*sqrt(3)) - log(2)/3. - Amiram Eldar, Jan 31 2023
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MATHEMATICA
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Transpose[NestList[{#[[2]], #[[3]], #[[1]]+3}&, {2, 3, 1}, 100]][[1]] (* Harvey P. Dale, Sep 08 2011 *)
LinearRecurrence[{1, 0, 1, -1}, {2, 3, 1, 5}, 100] (* Harvey P. Dale, Feb 02 2015 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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