A084962 Iterations of the Fibonacci sequence starting at 6.

6, 8, 21, 10946

Offset: 0

Author

Hollie L. Buchanan II, Jun 14 2003

Keywords

• nonn

Comments

The next term, a(4) = 1.695... * 10^2287, has 2288 digits and is too large to display.

This sequence is of interest because the sequences with this recurrence and a(0) in {0, 1, 2, 3, 4} all converge to 1 and the sequence with a(0) = 5 is constant.

Examples

			a(3) = Fibonacci(a(2)) = Fibonacci(21) = 10946.
		

Links

• Alonso del Arte, Table of a(n) for n=0..4, with digits of a(4) grouped in hundreds

Crossrefs

Cf. A000045, A007097, A010716 (starting with 5), A084963 (starting with 7).

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 6,
      (<<0|1>, <1|1>>^a(n-1))[1,2])
    end:
seq(a(n), n=0..4);  # Alois P. Heinz, May 09 2020

Mathematica

fibonaccieth6[m_] := Module[{ex = 6}, Do[ex = Fibonacci[ex], {m}]; ex] Table[fibonaccieth6[m], {m, 0, 4}]
NestList[Fibonacci[#] &, 6, 4] (* Alonso del Arte, Apr 30 2020 *)

Scala

val fiboLimited: LazyList[Int] = 0 #:: 1 #:: fiboLimited.zip(fiboLimited.tail).map { n => n._1 + n._2 }
def fibonaccieth(start: Int): LazyList[Int] = LazyList.iterate(start)(fiboLimited)
fibonaccieth(6).takeWhile( > 0).toList // _Alonso del Arte, Apr 30 2020

Formula

a(0) = 6, a(n) = Fibonacci(a(n-1)) for n>0.