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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 (list; graph; refs; listen; history; text; internal format)
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

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

EXAMPLE

a(3) = 5 because the 5 iterations to reach 1 are A006577(3) = 7; A006577(7) = 16; A006577(16) = 4; A006577(4) = 2; A006577(2) = 1.

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, `, it-1): 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, `, it-1):

    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

Cf. A006577.

Sequence in context: A147710 A153456 A021872 * A021196 A257406 A269980

Adjacent sequences:  A213195 A213196 A213197 * A213199 A213200 A213201

KEYWORD

nonn

AUTHOR

Michel Lagneau, Mar 01 2013

STATUS

approved

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Last modified August 12 10:31 EDT 2020. Contains 336438 sequences. (Running on oeis4.)