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A330588 a(n) is the first index m such that A330439(m) = n.

%I A330588 #12 Dec 13 2023 11:46:35
%S A330588 0,3,6,13,21,23,27,33,46,67,81,104,107,114,129,166,169,172,193,261,
%T A330588 267,276,287,311,373,430,457,478,485,590,596,656,691,768,789,796,873,
%U A330588 941,969,1047,1093,1149,1170,1239,1303,1349,1491,1533,1555,1567,1805,1808
%N A330588 a(n) is the first index m such that A330439(m) = n.
%H A330588 Alois P. Heinz, <a href="/A330588/b330588.txt">Table of n, a(n) for n = 1..16000</a>
%p A330588 b:= proc() 0 end:
%p A330588 g:= proc(n) option remember; local t;
%p A330588       t:= `if`(n<2, n, b(g(n-1))+b(g(n-2)));
%p A330588       b(t):= b(t)+1; t
%p A330588     end:
%p A330588 f:= proc(n) option remember; b(g(n)) end:
%p A330588 a:= proc() local l, t; t, l:= -1, proc() -1 end;
%p A330588       proc(k) local h;
%p A330588         while l(k)<0 do t:= t+1; h:= f(t);
%p A330588           if l(h)<0 then l(h):= t fi
%p A330588         od: l(k)
%p A330588       end
%p A330588     end():
%p A330588 seq(a(n), n=1..60);
%t A330588 b[_] = 0;
%t A330588 g[n_] := g[n] = Module[{t}, t = If[n < 2, n, b[g[n-1]] + b[g[n-2]]]; b[t]++; t];
%t A330588 f[n_] := f[n] = b[g[n]];
%t A330588 A[n_, k_] := Module[{l, t = -1, h}, l[_] = {}; While[Length[l[k]] < n, t++; h = f[t]; AppendTo[l[h], t]]; l[k][[n]]];
%t A330588 a[k_] := A[1, k];
%t A330588 Table[a[n], {n, 1, 60}] (* _Jean-François Alcover_, Dec 13 2023, after _Alois P. Heinz_ *)
%Y A330588 Row n=1 of A330587.
%Y A330588 Cf. A316774, A330439.
%K A330588 nonn
%O A330588 1,2
%A A330588 _Alois P. Heinz_, Dec 18 2019