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A112866 If a(n-1) is the i-th Fibonacci number then a(n)=Fibonacci(i+a(n-2)); with a(1)=1, a(2)=2 and where we use the following nonstandard indexing for the Fibonacci numbers: f(n)=f(n-1)+f(n-2), f(1)=1, f(2)=2 (cf. A000045).

%I A112866 #16 Oct 26 2023 08:26:49
%S A112866 1,2,3,8,34,1597,20365011074
%N A112866 If a(n-1) is the i-th Fibonacci number then a(n)=Fibonacci(i+a(n-2)); with a(1)=1, a(2)=2 and where we use the following nonstandard indexing for the Fibonacci numbers: f(n)=f(n-1)+f(n-2), f(1)=1, f(2)=2 (cf. A000045).
%C A112866 The next term has 345 digits and is not displayed here.
%e A112866 a(5)=Fibonacci(5+3)=34 because a(4) is the 5th Fibonacci number and a(3)=3.
%p A112866 f := proc(n)
%p A112866     combinat[fibonacci](n+1) ;
%p A112866 end proc:
%p A112866 Fidx := proc(n)
%p A112866     for i from 1 do
%p A112866         if f(i) = n then
%p A112866             return i;
%p A112866         elif f(i) > n then
%p A112866             return -1 ;
%p A112866         end if;
%p A112866     end do:
%p A112866 end proc:
%p A112866 A112866 := proc(n)
%p A112866     option remember;
%p A112866     if n<= 2 then
%p A112866         n;
%p A112866     else
%p A112866         i := Fidx(procname(n-1)) ;
%p A112866         f( i+procname(n-2)) ;
%p A112866     end if:
%p A112866 end proc: # _R. J. Mathar_, Nov 26 2011
%t A112866 f[n_] := Fibonacci[n+1];
%t A112866 Fidx[n_] := For[i = 1, True, i++, If[f[i] == n, Return[i], If[f[i] > n, Return[-1]]]];
%t A112866 a[n_] := a[n] = If[n <= 2, n, i = Fidx[a[n-1]]; f[i+a[n-2]]];
%t A112866 Table[a[n], {n, 1, 7}] (* _Jean-François Alcover_, Oct 26 2023, after _R. J. Mathar_ *)
%Y A112866 Cf. A112237, A000045, A112601.
%K A112866 nonn
%O A112866 1,2
%A A112866 _Yasutoshi Kohmoto_, Dec 25 2005