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

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, 37, 22, 35, 34, 55, 20, 32, 31, 50, 30, 48, 47, 76, 28, 45, 44, 71, 43, 69, 68, 110, 25, 40, 39, 63, 38, 61, 60, 97, 36, 58, 57, 92, 56, 90, 89, 144, 33, 53, 52

Offset: 1

Author

Clark Kimberling, Nov 26 2013

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Clark Kimberling)
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A232559, A000045.

Programs

Maple

g:= proc() local l, s; l, s:= [1], {1}:
      proc(n) option remember; local i, r; r:= l[1];
        l:= subsop(1=NULL, l);
        for i in [1+r, r+r] do if not i in s then
          l, s:=[l[], i], s union {i} fi
        od; r
      end
    end():
a:= proc() local t, a; t, a:= 0, proc() -1 end;
      proc(n) local h;
        while a(n) < 0 do
          t:= t+1; h:= g(t);
          if a(h) < 0 then a(h):= t fi
        od; a(n)
      end
    end():
seq(a(n), n=1..100);  # Alois P. Heinz, Sep 14 2021

Mathematica

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 *)
Table[Length[g1[n]], {n, 1, z}] (* Fibonacci numbers *)
t1 = Flatten[Table[Position[t, n], {n, 1, 200}]]  (* A232560 *)