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

1,2

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..1024

Index entries related to the 3x+1 (Collatz) problem

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A006370, A135282, A226123.

Sequence in context: A036164 A076536 A110009 * A348007 A025586 A087251

Adjacent sequences: A232500 A232501 A232502 * A232504 A232505 A232506

Keyword

nonn

Author

Lance Luttrell, Nov 24 2013

Status

approved