import math
print ("This program looks for secquences of consecutive numbers whose Collatz chains do not end in the cycle 5 > 16 > 8 > 4 > 2 > 1.")
print("""Please input a top bound and a sequence length.
The program will print out all sequences of numbers at least as long as the sequence length
found below the boundary number.
For the love of God either have a low top bound or a high sequence length.""")

topbound = int(input('Please input the top bound \n > '))
seqlength = int(input('Please input the minimum sequence length: \n > '))
adecouslist = []

for i in range (1, topbound + 1): # This runs each number within the bound through its Collatz steps. If it doesn't have a 5 in its history, it gets appended to magiclist.
    currentnum = i
    pathlist = []
    pathlist.append(currentnum) #start with the starting number--starts with 1)
    while currentnum != 1: # all collatz chains end in 1, or so the conjecture says, so you stop there
        if currentnum % 2 == 0: # if it's even...
            currentnum = int( currentnum / 2) # divide it by two
            pathlist.append(currentnum) # and add the new number to the list
        else: # otherwise, it's going to be odd
            currentnum = (currentnum * 3) + 1 # multiply by three and add one
            pathlist.append(currentnum)

    if 5 not in pathlist and (pathlist[0] & (pathlist[0]-1) != 0):
        adecouslist.append(pathlist[0])
    else: pass

seqlist = []
seqdict = {}
seqlengthnum = [] # this is a list of all numbers that *begin* a sequence of at least n long
for i in range(0, len(adecouslist)-1):
    if adecouslist[i+1] - adecouslist[i] == 1: # if 85-84 == 1, which it does: ...if 113 - 85 is 1, which it isn't...
        seqlist.append(adecouslist[i]) # append 84
    elif adecouslist[i+1] - adecouslist[i] != 1 and adecouslist [i] - adecouslist [i-1] == 1: # and... 113-85 ain't 1, but
        seqlist.append(adecouslist[i])
        if len(seqlist) >= seqlength:
            seqdict[seqlist[0]] = len(seqlist) # Creates an entry in dictionary seqdict.
            # The key in seqdict is the first number of the sequence, and the value is the length.
            seqlengthnum.append(seqlist[0])
        seqlist.clear()

seqlengthval = [] # the lengths of sequences

for number in (seqlengthnum):
    seqlengthval.append(seqdict[number])

sortedlengths = seqlengthval.copy()
sortedlengths.sort() # these are the lengths in ascending order

toplength = max(sortedlengths) + 1
bottomlength = min(sortedlengths)
for k in range(bottomlength, toplength):
    for j in seqlengthnum:
        if seqdict[j] == k:
            print(f'There is an adecous sequence of length {k} starting at {j}')