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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A220421 Number of halving and tripling steps to reach the largest value in the Collatz (3x+1) trajectory of n. 3
0, 0, 3, 0, 1, 4, 5, 0, 8, 2, 3, 5, 1, 6, 7, 0, 1, 9, 3, 0, 1, 4, 5, 0, 6, 2, 77, 7, 1, 8, 72, 0, 1, 2, 3, 10, 1, 4, 10, 0, 75, 2, 3, 5, 1, 6, 70, 0, 1, 7, 3, 0, 1, 78, 78, 0, 6, 2, 8, 9, 1, 73, 73, 0, 1, 2, 3, 0, 1, 4, 68, 0, 81, 2, 3, 5, 1, 11, 7, 0, 1, 76 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n) = 0 if n is a power of 2, as a(1) = a(2) = a(4) = ... = 0; however a(20) = a(24) = ... = 0 also and as such the condition (n = 2^k, k>=0) is sufficient but not necessary for a(n) = 0.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A087225(n) - 1.

EXAMPLE

a(3) = 3 because the Collatz trajectory for 3 is [3, 10, 5, 16, 8, 4, 2, 1], reaching the largest term, 16, in three steps.

a(4) = 0 because the Collatz trajectory only goes down from 4.

a(20) = 0: 20 is the largest term in [20, 10, 5, 16, 8, 4, 2, 1].

MATHEMATICA

Collatz[n_] :=NestWhileList[If[EvenQ[#], #/2, 3*# + 1] &, n, # > 1 &]; Table[Position[Collatz[n], Max[Collatz[n]]] - 1, {n, 82}](* Jayanta Basu, Mar 24 2013 *)

CROSSREFS

Cf. A006577, A014682, A025586.

Sequence in context: A143949 A124323 A250104 * A106683 A139601 A213191

Adjacent sequences:  A220418 A220419 A220420 * A220422 A220423 A220424

KEYWORD

nonn

AUTHOR

Jayanta Basu, Feb 19 2013

EXTENSIONS

More terms from Alois P. Heinz, Feb 20 2013

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 16 04:44 EDT 2021. Contains 345056 sequences. (Running on oeis4.)