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 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. 20
 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, Collatz Problem Wikipedia, Collatz conjecture 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

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Last modified October 23 16:15 EDT 2018. Contains 316529 sequences. (Running on oeis4.)