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