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A232560 Inverse permutation of the sequence of positive integers at A232559.

%I A232560 #9 Sep 14 2021 14:59:43
%S A232560 1,2,3,4,6,5,8,7,11,10,16,9,14,13,21,12,19,18,29,17,27,26,42,15,24,23,
%T A232560 37,22,35,34,55,20,32,31,50,30,48,47,76,28,45,44,71,43,69,68,110,25,
%U A232560 40,39,63,38,61,60,97,36,58,57,92,56,90,89,144,33,53,52
%N A232560 Inverse permutation of the sequence of positive integers at A232559.
%H A232560 Alois P. Heinz, <a href="/A232560/b232560.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Clark Kimberling)
%H A232560 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%p A232560 g:= proc() local l, s; l, s:= [1], {1}:
%p A232560       proc(n) option remember; local i, r; r:= l[1];
%p A232560         l:= subsop(1=NULL, l);
%p A232560         for i in [1+r, r+r] do if not i in s then
%p A232560           l, s:=[l[], i], s union {i} fi
%p A232560         od; r
%p A232560       end
%p A232560     end():
%p A232560 a:= proc() local t, a; t, a:= 0, proc() -1 end;
%p A232560       proc(n) local h;
%p A232560         while a(n) < 0 do
%p A232560           t:= t+1; h:= g(t);
%p A232560           if a(h) < 0 then a(h):= t fi
%p A232560         od; a(n)
%p A232560       end
%p A232560     end():
%p A232560 seq(a(n), n=1..100);  # _Alois P. Heinz_, Sep 14 2021
%t A232560 z = 12; g[1] = {1}; g[2] = {2}; g[n_] := Riffle[g[n - 1] + 1, 2 g[n - 1]]; j[2] = Join[g[1], g[2]]; j[n_] := Join[j[n - 1], g[n]]; g1[n_] := DeleteDuplicates[DeleteCases[g[n], Alternatives @@ j[n - 1]]]; g1[1] = g[1]; g1[2] = g[2]; t = Flatten[Table[g1[n], {n, 1, z}]]  (* A232559 *)
%t A232560 Table[Length[g1[n]], {n, 1, z}] (* Fibonacci numbers *)
%t A232560 t1 = Flatten[Table[Position[t, n], {n, 1, 200}]]  (* A232560 *)
%Y A232560 Cf. A232559, A000045.
%K A232560 nonn,easy
%O A232560 1,2
%A A232560 _Clark Kimberling_, Nov 26 2013