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+--- Thread: How can I found how many numbers are there in a Collatz Sequence that I found? (/thread-31024.html)
How can I found how many numbers are there in a Collatz Sequence that I found? - cananb - Nov-18-2020
I tried to find the longest starting value less than 100,000 in a Collatz Sequence. Actually, I have two questions:
1)Output is 77,031, is this correct?
2)How can I find how many elements are there in the sequence that I found?
def sequence_number(n):
term = 1
while n > 1:
if n % 2 == 0:
n = n/2
else:
n = 3 * n+1
term += 1
return term
def starting_number():
t = 0
x = 1
while x < 100000:
if sequence_number(x) > t:
t = sequence_number(x)
value = x
x += 1
return value
print("It starts with the number:", starting_number())
RE: How can I found how many numbers are there in a Collatz Sequence that I found? - DPaul - Nov-19-2020
Hi i see some potential issues:
- Indentation in the functions cannot be right
-you seem to be returning (line17) the value, rather than t.
Tell us what the max sequence is. Less than 77031 ?
Paul
RE: How can I found how many numbers are there in a Collatz Sequence that I found? - DeaD_EyE - Nov-19-2020
The result seems to be right. Just your indentation is wrong. For infinite sequences (collatz is one of them) Generators could be used.
Here is a derivation of your code:
from itertools import count
def ask_int(question):
while True:
user_input = input(question + ": ")
try:
return int(user_input)
except ValueError:
print(f"'{user_input}' is not a valid integer")
def collatz_generator(start):
if start < 1:
raise ValueError("Start must be a positive integer")
n = start
while n > 1:
if n % 2 == 0:
n = n // 2
else:
n = 3 * n + 1
yield n
def collatz_counter(start):
if start < 1:
raise ValueError("Start must be a positive integer")
n = start
for trys in count(1):
if n % 2 == 0:
n = n // 2
else:
n = 3 * n + 1
if n <= 1:
break
return trys
def longest_collatz(start=1, end=100_000):
maximum_length = 0
maximum_value = 0
for value in range(start, end + 1):
length = collatz_counter(value)
if length > maximum_length:
maximum_length = length
maximum_value = value
return maximum_value, maximum_length
if __name__ == "__main__":
print("Find the longest collatz sequence with given start and end")
start = ask_int("Start Value")
end = ask_int("End Value")
value, length = longest_collatz(start, end)
print(f"The start value {value} creates a collatz sequence with {length} values.")Quote:PS C:\Users\Admin\Desktop> py collatz.py
Find the longest collatz sequence with given start and end
Start Value: 1
End Value: 100_000
The start value 77031 creates a collatz sequence with 350 values.
PS C:\Users\Admin\Desktop> py collatz.py
Find the longest collatz sequence with given start and end
Start Value: 1
End Value: 1_000_000
The start value 837799 creates a collatz sequence with 524 values.
I think the code is also a bit faster.
The generator collatz_generator is not used in the code. I didn't remove it. Maybe you can experiment with it.
gen = collatz_generator(19) print(list(gen))
In [1]: gen = collatz_generator(19) ...: print(list(gen)) [58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1]The 19 is not included. My mistake. Quick fix just for completeness:
def collatz_generator(start):
if start < 1:
raise ValueError("Start must be a positive integer")
n = start
yield n # <-- this will yield n, which is the start value
while n > 1:
if n % 2 == 0:
n = n // 2
else:
n = 3 * n + 1
yield n # <-- this here are the values after the start value
RE: How can I found how many numbers are there in a Collatz Sequence that I found? - DPaul - Nov-19-2020
@DeaD_EyE:
I thought we were looking for the most iterations,
but we are looking for the value that causes them, indeed 77031!
Paul
RE: How can I found how many numbers are there in a Collatz Sequence that I found? - DeaD_EyE - Nov-19-2020
Quote:The start value 77031 creates a collatz sequence with 350 values.
Yes, we're looking for the most iterations (sequence length).
Given is start value from 1 to 100_000 for example.
Calculate for each start value, the collatz sequence length.
Take the longest sequence and tell us the start value.
In collatz_counter I count the iterations (hopefully right).
In longest_collatz I calculate the maximum_length (sequence length / iterations) and the corresponding start value to get this maximum length.
By the way, negative values are also possible for a collatz sequence. In this case the addition of 1 changed to subtraction.
Just for completeness:
def collatz_generator(start):
n = start
if n < 0:
offset = -1
else:
offset = +1
yield start
while abs(n) > 1:
if n % 2 == 0:
n = n // 2
else:
n = 3 * n + offset
yield n
RE: How can I found how many numbers are there in a Collatz Sequence that I found? - cananb - Nov-23-2020
(Nov-19-2020, 09:20 AM)DPaul Wrote: @DeaD_EyE:
I thought we were looking for the most iterations,
but we are looking for the value that causes them, indeed 77031!
Paul
I really appreciate your help!! Thank you so much