A226123 Number of terms of the form 2^k in Collatz(3x+1) trajectory of n.

1, 2, 5, 3, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 7, 9, 5, 5

Offset: 1

Author

Jayanta Basu, May 27 2013

Keywords

• nonn

Comments

a(n) = sum(A209229(A070165(n,k)): k=1..A006577(n)). - Reinhard Zumkeller, May 30 2013

Examples

			a(3)=5 since Collatz trajectory of 3 contains terms 1,2,4,8 and 16.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A070165.

Cf. A135282, A208981.

Programs

Haskell

a226123 = sum . map a209229 . a070165_row
-- Reinhard Zumkeller, May 30 2013

Mathematica

coll[n_]:=NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&]; Table[Length[Select[coll[n],IntegerQ[Log[2,#]]&]],{n,87}]