A275748 Number of Fibonacci numbers in {n, f(n), f(f(n)), ...., 1}, where f is the Collatz function.

1, 2, 5, 2, 4, 5, 6, 3, 6, 4, 6, 5, 5, 6, 4, 3, 5, 6, 6, 4, 4, 6, 4, 5, 6, 5, 6, 6, 6, 4, 6, 3, 6, 6, 4, 6, 6, 6, 7, 4, 6, 4, 6, 6, 6, 4, 6, 5, 6, 6, 6, 5, 4, 6, 7, 6, 6, 6, 7, 4, 4, 6, 6, 3, 6, 6, 6, 6, 5, 4, 6, 6, 7, 6, 3, 6, 6, 7, 6, 4, 4, 6, 6, 4, 3, 6, 6, 6, 7, 6, 6, 4, 4, 6, 6, 5, 7, 6, 6, 6

Offset

1,2

Comments

Or number of Fibonacci numbers in the trajectory of n under the 3x+1 map (i.e. the number of Fibonacci numbers until the trajectory reaches 1).

Links

Table of n, a(n) for n=1..100.

Example

The finite sequence n, f(n), f(f(n)), ...., 1 for n = 9 is: 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1 which has six Fibonacci numbers {1, 2, 5, 8, 13, 34}. Hence a(9) = 6.

Mathematica

s = Fibonacci /@ Range@ 20; Table[Length@ Select[Union@ NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, n, # != 1 &], MemberQ[s, #] &], {n, 120}] (* Michael De Vlieger, Aug 07 2016 *)

Prog

(PARI) print1(1, ", "); for(n=2, 100, s=n; t=1; while(s!=1, if(issquare(5*s^2+4) ||issquare(5*s^2-4), t++, t=t); if(s%2==0, s=s/2, s=(3*s+1)); if(s==1, print1(t, ", "); ); ))

Crossrefs

Cf. A006577.

Sequence in context: A187788 A085072 A077200 * A375909 A216625 A122581

Adjacent sequences: A275745 A275746 A275747 * A275749 A275750 A275751

Keyword

nonn,easy

Author

Michel Lagneau, Aug 07 2016

Status

approved