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A260389 For the Collatz (3x+1) iteration starting at k, the sequence lists the smallest k such that Fibonacci(n) belongs to the trajectory of k, or 0 if no such k exists. 1
2, 2, 3, 6, 3, 3, 7, 42, 7, 73, 39, 288, 27, 27, 135, 1974, 1419, 861, 2787, 13530, 7297, 5247, 33963, 92736, 100033, 161857, 116395 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The initial term k is not counted as an element of the trajectory.

LINKS

Table of n, a(n) for n=1..27.

EXAMPLE

a(1)=a(2)=2 because 1 = Fibonacci(1)=Fibonacci(2) is in the trajectory 2 -> 1;

a(3)=3 because 2 = Fibonacci(3) is in the trajectory 3 -> 10 -> 5 -> ... -> 2 ->1;

a(4)=6 because 7 = Fibonacci(4)=3 is in the trajectory 6 -> 3 -> 10 -> ... -> 1;

a(5)=3 because 5 = Fibonacci(5)=3 is in the trajectory 3 -> 10 -> 5 -> ... -> 1.

a(6)=3 because 8 = Fibonacci(6)=3 is in the trajectory 3 -> 10 -> 5 -> 16 -> 8 -> ... -> 1;

a(7)=7 because 13 = Fibonacci(7)=3 is in the trajectory 7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> ... -> 1.

MAPLE

with(numtheory):with(combinat, fibonacci):

for n from 1 to 10000 do:

jj:=0:

for k from 2 to 10^8 while(jj=0) do:

lst:={}:m:=k:ii:=0:it:=10^6:

   for i from 1 to it while(ii=0) do:

    if irem(m, 2)=0

    then

    m:=m/2:

    else m:=3*m+1:

    fi:

    lst:=lst union {m}:

     if m=1

     then

     ii:=1:

     else

     fi:

   od:

    n0:=nops(lst):

    for j from 1 to n0 while(jj=0)do:

     if fibonacci(n)=lst[j]

     then

     jj:=1:

     else fi:

    od:

     if jj=1 then printf("%d %d \n", n, k):

     else fi:

    od:od:

CROSSREFS

Cf. A000045, A006577.

Sequence in context: A284785 A076333 A015051 * A291372 A064426 A051173

Adjacent sequences:  A260386 A260387 A260388 * A260390 A260391 A260392

KEYWORD

nonn,hard

AUTHOR

Michel Lagneau, Nov 22 2015

STATUS

approved

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Last modified June 20 00:47 EDT 2019. Contains 324223 sequences. (Running on oeis4.)