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A229120
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Inverse of permutation A229119.
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2
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1, 3, 2, 7, 6, 5, 15, 14, 4, 13, 10, 31, 30, 12, 29, 9, 26, 21, 63, 62, 28, 61, 8, 25, 58, 11, 18, 53, 42, 127, 126, 60, 125, 24, 57, 122, 17, 27, 50, 117, 22, 37, 106, 85, 255, 254, 124, 253, 56, 121, 250, 16, 49, 59, 114, 245, 19, 34, 54, 101, 234, 20, 45, 74, 213, 170, 511, 510, 252, 509, 120, 249, 506, 48
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OFFSET
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1,2
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COMMENTS
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Defines an infinite permutation on the integers, containing cycles of infinite length, but with an inverse (A229119) that can be generated.
The least integer producing an infinite cycle is n=4: {4, 7, 15, 29, 42, 37, 17, 26, 11, 10, 13, 30, 127, 77, 242, 266, 173, 205, 2034, 6474, ...}.
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LINKS
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EXAMPLE
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MATHEMATICA
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<< Combinatorica`; unrankpartition[n_Integer, k_Integer] := Block[{ove, res, qq, zz, mem}, ove=PartitionsP[n]-k; res={}; While[n-Tr[res]>0, qq=0; zz=0; While[(mem=NumberOfPartitions[n-Tr[res], qq + 1]) <= ove, zz = mem; qq++]; AppendTo[res, qq + 1]; ove = ove-zz]; res] /; k <= PartitionsP[n] && k > 0; unrankpartition[n_Integer, All]:=Block[{k=1, z}, While[( z=Tr[PartitionsP[Range@k]])<n, k++]; unrankpartition[k, PartitionsP[k]+n-z]]; par2int[par_?PartitionQ]:=Block[{t3, t4, t5}, t3=Differences[Prepend[Reverse[par], 0]]; t4=Reverse@MapAt[#-1&, 1+t3, 1]; t5=Flatten[Table[Mod[k, 2]+0*Range[t4[[k]]], {k, Length[t4]}]]; FromDigits[t5, 2]]; b = Table[par2int@unrankpartition[n, All], {n, 138}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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