A112866 - OEIS

%I #16 Oct 26 2023 08:26:49

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

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

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

%p f := proc(n)

%p     combinat[fibonacci](n+1) ;

%p end proc:

%p Fidx := proc(n)

%p     for i from 1 do

%p         if f(i) = n then

%p             return i;

%p         elif f(i) > n then

%p             return -1 ;

%p         end if;

%p     end do:

%p end proc:

%p A112866 := proc(n)

%p     option remember;

%p     if n<= 2 then

%p         n;

%p     else

%p         i := Fidx(procname(n-1)) ;

%p         f( i+procname(n-2)) ;

%p     end if:

%p end proc: # _R. J. Mathar_, Nov 26 2011

%t f[n_] := Fibonacci[n+1];

%t Fidx[n_] := For[i = 1, True, i++, If[f[i] == n, Return[i], If[f[i] > n, Return[-1]]]];

%t a[n_] := a[n] = If[n <= 2, n, i = Fidx[a[n-1]]; f[i+a[n-2]]];

%t Table[a[n], {n, 1, 7}] (* _Jean-François Alcover_, Oct 26 2023, after _R. J. Mathar_ *)

%Y Cf. A112237, A000045, A112601.

%K nonn

%O 1,2

%A _Yasutoshi Kohmoto_, Dec 25 2005