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A159999 Number of numbers not greater than n occurring in Collatz (3x+1) trajectory starting with n. 7
1, 2, 3, 3, 4, 6, 5, 4, 7, 6, 7, 9, 7, 10, 7, 5, 9, 14, 11, 8, 6, 12, 9, 11, 14, 10, 10, 16, 14, 11, 10, 6, 17, 12, 9, 20, 18, 17, 18, 9, 13, 8, 20, 16, 14, 12, 13, 12, 20, 21, 18, 12, 10, 18, 15, 20, 24, 19, 22, 16, 14, 17, 15, 7, 23, 25, 22, 15, 13, 12, 16, 23 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) < n for n>6;

a(A033496(n)) = A008908(A033496(n)).

a(n) = n - A246436(n); row lengths of triangle A214614. - Reinhard Zumkeller, Sep 01 2014

LINKS

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

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

FORMULA

a(n) = f(n,n,1) with f(n,m,x) = if m=1 then x else f(n, A006370(m), if A006370(m)<n then x+1 else x).

EXAMPLE

a(9) = #{1,2,4,5,7,8,9} = 7, as

9-28-14-7-22-11-34-17-52-26-13-40-20-10-5-16-8-[4-2-1]*

9-..-..-7-..-..-..-..-..-..-..-..-..-..-5-..-8-[4-2-1]*.

MATHEMATICA

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; f[n_] := Module[{c = Collatz[n]}, Length[Select[c, # <= n &]]]; Table[ f[n], {n, 100}] (* T. D. Noe, Mar 07 2013 *)

PROG

(Haskell)

a159999 n = length $ takeWhile (<= n) $ sort $ a070165_row n

-- Reinhard Zumkeller, Sep 01 2012

CROSSREFS

Cf. A033496, A008908, A070165, A214614.

Sequence in context: A203291 A220053 A320509 * A003977 A003971 A282442

Adjacent sequences:  A159996 A159997 A159998 * A160000 A160001 A160002

KEYWORD

nonn,look

AUTHOR

Reinhard Zumkeller, May 04 2009

STATUS

approved

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Last modified October 22 01:42 EDT 2018. Contains 316431 sequences. (Running on oeis4.)