A112601 -id:A112601 - cp's OEIS frontend

A112237 If a(n-2) is the i-th Fibonacci number then a(n)=Fibonacci(i+a(n-1)); 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, 144, 9969216677189303386214405760200

Offset: 1

Yasutoshi Kohmoto, Dec 22 2005

nonn

The next term, a(7)=f(9969216677189303386214405760211), has tens of thousands of digits at least and is too large to include. - R. J. Mathar, Oct 14 2006

			a(5)=Fibonacci(3+8)=144 because a(3) is third Fibonacci number and a(4)=8.

Cf. A000045, A112601.

a(6)=f(149) from R. J. Mathar, Oct 14 2006

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).

Original entry on oeis.org

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

Offset: 1

Yasutoshi Kohmoto, Dec 25 2005

nonn

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

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

Cf. A112237, A000045, A112601.

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

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 *)

cp's OEIS Frontend

A112237 If a(n-2) is the i-th Fibonacci number then a(n)=Fibonacci(i+a(n-1)); 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).

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