login
This site is supported by donations to The OEIS Foundation.

 

Logo

"Email this user" was broken Aug 14 to 9am Aug 16. If you sent someone a message in this period, please send it again.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A078719 Number of odd terms among n, f(n), f(f(n)), ...., 1 for the Collatz function (that is, until reaching "1" for the first time), or -1 if 1 is never reached. 19
1, 1, 3, 1, 2, 3, 6, 1, 7, 2, 5, 3, 3, 6, 6, 1, 4, 7, 7, 2, 2, 5, 5, 3, 8, 3, 42, 6, 6, 6, 40, 1, 9, 4, 4, 7, 7, 7, 12, 2, 41, 2, 10, 5, 5, 5, 39, 3, 8, 8, 8, 3, 3, 42, 42, 6, 11, 6, 11, 6, 6, 40, 40, 1, 9, 9, 9, 4, 4, 4, 38, 7, 43, 7, 4, 7, 7, 12, 12, 2, 7, 41, 41, 2, 2, 10, 10, 5, 10, 5, 34, 5, 5, 39 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The Collatz function (related to the "3x+1 problem") is defined by: f(n) = n/2 if n is even; f(n) = 3n + 1 if n is odd. A famous conjecture states that n, f(n), f(f(n)), .... eventually reaches 1.

a(n) = A006667(n) + 1; a(A000079(n))=1; a(A062052(n))=2; a(A062053(n))=3; a(A062054(n))=4; a(A062055(n))=5; a(A062056(n))=6; a(A062057(n))=7; a(A062058(n))=8; a(A062059(n))=9; a(A062060(n))=10. - Reinhard Zumkeller, Oct 08 2011

The count includes also the starting value n if it is odd. See A286380 for the version which never includes n itself. - Antti Karttunen, Aug 10 2017

LINKS

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

Chris K. Caldwell and G. L. Honaker, Jr., Prime curio for 41 (which says 41 is a fixed point)

Eric Weisstein's World of Mathematics, CollatzProblem

Wikipedia, Collatz conjecture

Index entries for sequences related to 3x+1 (or Collatz) problem

FORMULA

a(n) = A286380(n) + A000035(n). - Antti Karttunen, Aug 10 2017

EXAMPLE

The terms n, f(n), f(f(n)), ...., 1 for n = 12 are: 12, 6, 3, 10, 5, 16, 8, 4, 2, 1, of which 3 are odd. Hence a(12) = 3.

MATHEMATICA

f[n_] := Module[{a, i, o}, i = n; o = 1; a = {}; While[i > 1, If[Mod[i, 2] == 1, o = o + 1]; a = Append[a, i]; i = f[i]]; o]; Table[f[i], {i, 1, 100}]

Table[Count[NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &], _?OddQ], {n, 94}] (* Jayanta Basu, Jun 15 2013 *)

PROG

(Haskell)

a078719 =

   (+ 1) . length . filter odd . takeWhile (> 2) . (iterate a006370)

a078719_list = map a078719 [1..]

-- Reinhard Zumkeller, Oct 08 2011

CROSSREFS

Cf. A006370, A014682, A078720, A139391, A286380.

Sequence in context: A138881 A070983 A078350 * A087227 A060477 A175945

Adjacent sequences:  A078716 A078717 A078718 * A078720 A078721 A078722

KEYWORD

nonn,changed

AUTHOR

Joseph L. Pe, Dec 20 2002

EXTENSIONS

"Escape clause" added to definition by N. J. A. Sloane, Jun 06 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified August 18 18:20 EDT 2017. Contains 290738 sequences.