A185023 Number of steps to reach the number 1 of the map n -> n/3 if x==0 (mod 3), n -> (4n-1)/3 if x==1 (mod 3), n -> (4n+1)/3 if x==2 (mod 3).

0, 2, 1, 5, 4, 3, 3, 7, 2, 21, 6, 6, 20, 10, 5, 5, 19, 4, 9, 4, 4, 23, 18, 8, 8, 8, 3, 27, 22, 22, 17, 12, 7, 7, 7, 7, 26, 21, 21, 16, 16, 11, 11, 11, 6, 6, 6, 6, 25, 20, 20, 20, 15, 5, 15, 10, 10, 10, 10, 5, 5, 29, 5, 24, 24, 24, 19, 19, 19, 19, 14, 9, 14, 9

Offset

1,2

Comments

A variation of the "3x+1" problem. - T. D. Noe, Feb 06 2012

Links

Michel Lagneau, Table of n, a(n) for n = 1..10000

Example

a(8) = 7 because the trajectory of 8  is  8 -> 11 -> 15 -> 5 -> 7-> 9 -> 3-> 1 with 7 iterations.

Maple

T:=array(0..2):for n from 1 to 100 do:ii:=0:n0:=n: i:=0:for it from 1 to 100 while(ii=0) do:T[0]:=n0/3: T[1]:=(4*n0-1)/3: T[2]:=(4*n0+1)/3:r:=irem(n0, 3):n0:=T[r]: i:=i+1:if n0=1 then ii:=1: else fi:od: printf(`%d, `, i):od:

Mathematica

nxt[n_]:=Module[{m=Mod[n, 3]}, Which[m==0, n/3, m==1, (4n-1)/3, m==2, (4n+1)/3]]; Table[Length[NestWhileList[nxt, n, #!=1&]]-1, {n, 80}] (* Harvey P. Dale, Jul 20 2013 *)

Crossrefs

Cf. A006577 (3x+1 problem).

Sequence in context: A275183 A275131 A280513 * A061579 A094064 A343809

Adjacent sequences: A185020 A185021 A185022 * A185024 A185025 A185026

Keyword

nonn

Author

Michel Lagneau, Feb 04 2012

Status

approved