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A229120 Inverse of permutation A229119.

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%I A229120 #20 Mar 09 2024 01:45:44
%S A229120 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,
%T A229120 18,53,42,127,126,60,125,24,57,122,17,27,50,117,22,37,106,85,255,254,
%U A229120 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
%N A229120 Inverse of permutation A229119.
%C A229120 Defines an infinite permutation on the integers, containing cycles of infinite length, but with an inverse (A229119) that can be generated.
%C A229120 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, ...}.
%H A229120 <a href="/index/Per#perm">Index entries for sequences related to permutations</a>
%e A229120 See A229119.
%t A229120 << 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}]
%Y A229120 Cf. A226062.
%K A229120 nonn
%O A229120 1,2
%A A229120 _Wouter Meeussen_, Sep 14 2013