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

%I #7 May 30 2013 11:03:17

%S 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,

%T 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,

%U 5,5,5,5,5,5,9,5,5,5,5,5,5,5,5,7,9,5,5

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

%C a(n) = sum(A209229(A070165(n,k)): k=1..A006577(n)). - _Reinhard Zumkeller_, May 30 2013

%H Reinhard Zumkeller, <a href="/A226123/b226123.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%o (Haskell)

%o a226123 = sum . map a209229 . a070165_row

%o -- _Reinhard Zumkeller_, May 30 2013

%Y Cf. A070165.

%Y Cf. A135282, A208981.

%K nonn

%O 1,2

%A _Jayanta Basu_, May 27 2013