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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
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
Sequence in context: A076333 A015051 A362199 * A291372 A064426 A051173
KEYWORD
nonn,hard
AUTHOR
Michel Lagneau, Nov 22 2015
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)