Weird maths problem
Posted: November 8th, 2020, 5:26 am
A friend forwarded me this problem that initially does not seem overly complicated to tackle but I have had a hard time with it and still no solution:
To check initially that this seems like it is the case, I wrote a simple Python script:
In this script, "listnumbers" is the list that contains all numbers m for which A(m)<A(m-1). As you can see, for the first 300 terms of sequence A, there are many. Running it for the first 3000 terms or so shows no sign of stopping.
I was thinking of trying to prove the opposite by induction (that there is a number Z such that for all m>Z, A(m)>(Am-1)) but it seems very complicated...
Any ideas?
Code: Select all
Sequence A(n) is defined as follows:
with t=1,
the following is done sequentially from i=1 to i=n:
if t is divisible by i: t+=i
else: t+=n
after the last iteration (i=n), A(n) is defined: A(n)=t
Prove that there exist infinitely many m such that A(m)<A(m-1)Code: Select all
olda=1
n=0
listnumbers=[]
while n<300:
a=1
for i in range(n):
if a%(i+1)==0:
a+=(i+1)
else:
a+=n
if olda>a:
listnumbers.append(n)
print(str(a))
olda=a
n+=1
print(listnumbers)I was thinking of trying to prove the opposite by induction (that there is a number Z such that for all m>Z, A(m)>(Am-1)) but it seems very complicated...
Any ideas?