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A229120
Inverse of permutation A229119.
2
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
OFFSET
1,2
COMMENTS
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, ...}.
EXAMPLE
See A229119.
MATHEMATICA
<< 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}]
CROSSREFS
Cf. A226062.
Sequence in context: A126316 A101224 A348366 * A255067 A139285 A080398
KEYWORD
nonn
AUTHOR
Wouter Meeussen, Sep 14 2013
STATUS
approved