A232503 Largest power of 2 in the Collatz (3x+1) trajectory of n.

1, 2, 16, 4, 16, 16, 16, 8, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 64, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 32, 16, 16, 16, 16, 16, 16, 16, 16, 16, 64, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 64, 16, 16, 16, 16

Offset: 1

Author

Lance Luttrell, Nov 24 2013

Keywords

• nonn

Comments

All terms are powers of 4 (A000302) unless n is an odd-indexed power of 2 (A004171), as explained in one of the comments for A135282. - Alonso del Arte, Nov 26 2013

Examples

			a(8) = 8 because then there are only halving steps and thus 8 is the largest power of 2 in its Collatz trajectory.
a(9) = 16 because the Collatz sequence for 9 goes 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1 (see A033479) and the largest power of 2 there is 16.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1024
• Index entries related to the 3x+1 (Collatz) problem

Crossrefs

Cf. A006370, A135282, A226123.

Programs

Mathematica

Collatz[n_?OddQ] := 3n + 1; Collatz[n_?EvenQ] := n/2; Table[NestWhile[Collatz, n, Not[IntegerQ[Log[2, #]]] &], {n, 64}] (* Alonso del Arte, Nov 26 2013 based on T. D. Noe's program for A135282 *)
Table[With[{p2=2^Range[0,10]},Select[NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n,#>1&], MemberQ[ p2,#]&]]//Max,{n,70}] (* Harvey P. Dale, May 07 2016 *)

Scheme

(define (A232503 n) (let loop ((n n) (m 1)) (if (= 1 n) m (loop (A006370 n) (if (= 1 (A209229 n)) (max n m) m)))))
(define (A006370 n) (if (even? n) (/ n 2) (+ 1 n n n)))
;; Antti Karttunen, Aug 18 2017

Formula

a(n) = 2^A135282(n). - Antti Karttunen, Aug 18 2017