

A213198


Number of iterations of the map n > f(f(f(...f(n)...))) to reach the end of the cycle, where f(n) = A006577(n), the initial number n is not counted.


1



0, 1, 5, 2, 0, 7, 4, 6, 7, 8, 11, 8, 8, 10, 10, 3, 9, 6, 6, 5, 5, 11, 11, 9, 12, 9, 13, 7, 7, 7, 10, 1, 10, 9, 9, 6, 6, 6, 10, 7, 11, 7, 8, 4, 4, 4, 10, 12, 10, 10, 10, 12, 12, 7, 7, 7, 2, 7, 2, 7, 7, 15, 15, 8, 14, 14, 14, 11, 11, 11, 14, 12, 12, 12, 11, 12
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OFFSET

1,3


COMMENTS

A006577 is the number of halving and tripling steps to reach 1 in '3x+1' problem.
The end of the cycle is 1 or 5 for n = 5, 32, 57, 59, 344, 346, 348, 349, ...


LINKS



EXAMPLE

a(5) = 0 because A006577(5) = 5 is the end of the cycle.
a(57) = 2 because A006577(57) = 32 and A006577(32) = 5 is the end of the cycle.


MAPLE

for n from 1 to 200 do:
m:=n: a:=2:
for it from 1 to 1000
while (a>1) do:
jj:=0: a:=0: x:=m:
if m=5 then
printf(`%d, `, it1): jj:=1:
else
for i from 1 to 1000
while (x>1) do:
if irem(x, 2)=0 then
x := x/2: a := a+1:
else
x := 3*x+1: a := a+1:
fi:
od:
m:=a:
fi:
od:
if jj=0 then
printf(`%d, `, it1):
fi:
od:


MATHEMATICA

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; f[n_] := Length[Collatz[n]]  1; Table[k = Rest[NestWhileList[f, n, UnsameQ, All]]; If[k[[1]] == n, 0, k = DeleteCases[k, 0]; If[Length[k] > 1 && k[[1]] == k[[2]], k = Most[k]]; Length[k]], {n, 100}] (* T. D. Noe, Mar 01 2013 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



