The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A078372 Number of squarefree integers in {n, f(n), f(f(n)), ...., 1}, where f is the Collatz function defined by f(x) = x/2 if x is even; f(x) = 3x + 1 if x is odd. 2
 1, 2, 5, 2, 3, 6, 11, 2, 12, 4, 9, 6, 5, 12, 11, 2, 7, 12, 13, 4, 3, 10, 9, 6, 14, 6, 74, 12, 11, 12, 71, 2, 15, 8, 7, 12, 13, 14, 23, 4, 73, 4, 17, 10, 8, 10, 69, 6, 14, 14, 15, 6, 5, 74, 73, 12, 19, 12, 21, 12, 11, 72, 72, 2, 15, 16, 17, 8, 7, 8, 67, 12, 75, 14, 6, 14, 13, 24, 23, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Number of squarefree terms in 3x+1 trajectory started at n. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 J. C. Lagarias, The 3x+1 problem and its generalizations, Amer. Math. Monthly, 92 (1985), 3-23. EXAMPLE The finite sequence n, f(n), f(f(n)), ...., 1 for n = 12 is 12, 6, 3, 10, 5, 16, 8, 4, 2, 1, which has six squarefree terms. Hence a(12) = 6. n=61: trajectory={61,184,92,46,23,70,35,...,20,10,5,16,8,4,2,1}, squarefree terms={61,46,23,70,35,106,53,10,5,2,1}, so a(61)=11. MATHEMATICA Table[Count[NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&], _?(SquareFreeQ)], {n, 80}] (* Harvey P. Dale, Oct 23 2011 *) CROSSREFS Sequence in context: A199611 A111232 A087892 * A154751 A299777 A197545 Adjacent sequences:  A078369 A078370 A078371 * A078373 A078374 A078375 KEYWORD nonn AUTHOR Joseph L. Pe, Dec 24 2002 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 11 14:29 EDT 2021. Contains 342886 sequences. (Running on oeis4.)