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).

1, 2, 3, 8, 34, 1597, 20365011074

Offset: 1

Author

Yasutoshi Kohmoto, Dec 25 2005

Keywords

• nonn

Comments

The next term has 345 digits and is not displayed here.

Examples

			a(5)=Fibonacci(5+3)=34 because a(4) is the 5th Fibonacci number and a(3)=3.
		

Crossrefs

Cf. A112237, A000045, A112601.

Programs

Maple

f := proc(n)
    combinat[fibonacci](n+1) ;
end proc:
Fidx := proc(n)
    for i from 1 do
        if f(i) = n then
            return i;
        elif f(i) > n then
            return -1 ;
        end if;
    end do:
end proc:
A112866 := proc(n)
    option remember;
    if n<= 2 then
        n;
    else
        i := Fidx(procname(n-1)) ;
        f( i+procname(n-2)) ;
    end if:
end proc: # R. J. Mathar, Nov 26 2011

Mathematica

f[n_] := Fibonacci[n+1];
Fidx[n_] := For[i = 1, True, i++, If[f[i] == n, Return[i], If[f[i] > n, Return[-1]]]];
a[n_] := a[n] = If[n <= 2, n, i = Fidx[a[n-1]]; f[i+a[n-2]]];
Table[a[n], {n, 1, 7}] (* Jean-François Alcover, Oct 26 2023, after R. J. Mathar *)