I wrote a little python script to do it for me:
l = (0,1,2,3,4,5)
hist = []
def getNext(l):
return (l[1],l[2],l[3],l[4],l[5],int(str(sum(l))[-1]))
for i in range(100000):
hist.append(l)
l = getNext(l)
print(l)
if l in hist:
print("DUPLICATE at {}".format(i))
break
if l == (1,3,5,7,9):
print("FOUND IT")
After 1456 iterations of this loop, we come back to the original 6 terms of the sequence and we still haven't encountered 13579.
I have no good mathematical answer for why this is true though...which I assume there is?
Actually I'm still trying to solve this myself. I really like the code. There could be a sequence of 2x+1 starting with x=0 and going to x=4 that is past 1456 iterations. The way to prove it would be to find a recurring cycle and show that this cannot be part of the cycle. What I'm trying to do right now is see if it has any pattern to it.
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That's what I'm saying I did...the code finds a cycle at the 1456th iteration
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