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
KEYWORD
nonn
AUTHOR
Wouter Meeussen, Sep 14 2013
STATUS
approved