A174429 Collatz-Fibonacci numbers: a(1) = a(2) = 1; if n > 2, a(n) = a(C(n)) + a(C(C(n))), where C(n) = A006370(n).

1, 1, 21, 2, 8, 34, 1597, 3, 6765, 13, 610, 55, 55, 2584, 2584, 5, 233, 10946, 10946, 21, 21, 987, 987, 89, 46368, 89, 114059301025943970552219, 4181, 4181, 4181, 10284720757613717413913, 8, 196418, 377, 377, 17711, 17711, 17711, 9227465, 34

Offset: 1

Author

Sam Alexander, Mar 19 2010

Keywords

• nonn
• nice
• look

Examples

			a(4) = a(2) + a(1) = 2. a(8) = a(4) + a(2) = 3. a(16) = a(8) + a(4) = 5. a(5) = a(16) + a(8) = 8.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Sam Alexander, Collatz Recursion

Programs

Haskell

a174429 = a000045 . a008908  -- Reinhard Zumkeller, Nov 10 2011

Mathematica

collatz[n_] := If[EvenQ[n], n/2, 3n + 1]; collFibo[1] = 1; collFibo[2] = 1; collFibo[n_] := collFibo[n] = collFibo[collatz[n]] + collFibo[collatz[collatz[n]]]; Table[collFibo[n], {n, 100}] (* T. D. Noe, Jul 06 2010 *)

Formula

a(n) = Fibonacci(A008908(n)) = A000045(A008908(n)). - T. D. Noe, Jul 06 2010

Extensions

Corrected by T. D. Noe, Jul 06 2010