SharedDoesItEnd.sagewsOpen in CoCalc
Author: Paul Zeitz
Views : 3
Description: sage worksheet for collatz conjecture June 21, 2016
# LINES BEGINNING WITH HASHTAG ARE 'COMMENTS'

# collatz (n) equals n/2 if n is even, 3n+1 if n is odd

def collatz(n):
if n%2 == 0:
return n/2
else:
return 3*n+1

# compute the inverse as a list (there may be one or two values)
def collatzInv(n):
if n%6==4:
return [2*n, (n-1)/3]
else:
return [2*n]

# give a list of successive iterations ending at 1
def collatzEvol(n):
next = collatz(n)
evol=[n,next]
while next <> 1:
next = collatz(next)
evol.append(next)
return evol

# make a list of inverses up to length "level"
def collatzInvEvol(n,level):
evol = [n]
while level>0:
for a in evol:
evol = union(evol, collatzInv(a))
level -= 1
return evol

# compute the length of the iteration
def collatzLength(n):
return len(collatzEvol(n))

#compute the 'max hailstone height'
def collatzMax(n):
return max(collatzEvol(n))

collatz(99)

298
#notice the

list_plot(collatzEvol(27), plotjoined=true)

collatzEvol(27)

[27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1]
maxi = [collatzMax(n) for n in [1..1000]]

list_plot(maxi,ymax= 10000)