Binary Complement Sequences and 22246 - Page 2

LaurV · 2020-02-10, 13:18

Moved to misc math. RDS is right, in spite of the fact that his "go back to the books" attitude is known here around, and so it is his sensitivity about what's posted in the Math subforum, and in spite of the fact that we consider his reaction a bit too exaggerated, it is misc math. Or it could be at best destined to the Puzzles thread (it actually can make a nice puzzle, and we'll like to play with it a little in the future... any takers?).

The OP stated clearly this is recreational for him, and he doesn't want to break any math boundaries with it. Moreover, no claim of solving Collatz was made, in fact, the two problems are barely related. Yet, this may be a nice puzzle...

Lack of knowledge does not make one stupid, and recognizing incompetence in a domain does not make one stupid, even if he wants or not to learn about. People have better thinks to do. I can't speak Japanese, and I don't want to learn it (well... I want, but I always find something better to do, and few trials in the past resulted in no progress, so I am still wondering if I am stupid or not... but don't tell that to these guys here...)

Boltzmann brain · 2020-02-10, 16:24

Honestly, I'm a little surprised that the result of the operation is on average 0.75 the size of the input. I'd have thought it would be a bit narrower than that, especially considering the size of some of the resultant numbers. Then again, with a large enough sample such variance should turn up stuff like this every so often. I wonder what the chance is of a number ~20000 reaching 1600 digits in 10M operations when on average each step is 0.75 the previous. That may or may not be easy to calculate.

Thanks for moving it LaurV, it does seem it would fit better here. I was disheartened by RDS's comments but I could understand where he was coming from. In truth, I did suffer minor traumatic flashes for the rest of the day but that's more a reflection of my fragile mental state (I have rather severe social anxiety, I am on medication so don't worry too much).

At the moment, the puzzle seems to be: does 22246 terminate? This is reminding me of the aliquot sequence of 276, though without the factoring thank goodness!

paulunderwood · 2020-02-10, 16:55

Quote:

Originally Posted by Boltzmann brain

Thanks for moving it LaurV, it does seem it would fit better here. I was disheartened by RDS's comments but I could understand where he was coming from. In truth, I did suffer minor traumatic flashes for the rest of the day but that's more a reflection of my fragile mental state (I have rather severe social anxiety, I am on medication so don't worry too much).

Keep your pecker up and don't succumb to Boltzmann's end, seriously. RDS is sometimes very critical, but, after all, he is one of The Greats in his field.

Uncwilly · 2020-02-11, 17:57

Quote:

Originally Posted by paulunderwood

Keep your pecker up and don't succumb to Boltzmann's end, seriously.

Your are referring to the OP's nose I suspect. Just to be clear that, using the nose refer to pecking, like a woodpecker's bill, is common in some areas. Other areas people shy away from that expression. They would say, "Keep your chin up". Pointing this out, as the forum is international and some might mistake the expression as something less savory.

paulunderwood · 2020-02-11, 18:06

Quote:

Originally Posted by Uncwilly

Your are referring to the OP's nose I suspect. Just to be clear that, using the nose refer to pecking, like a woodpecker's bill, is common in some areas. Other areas people shy away from that expression. They would say, "Keep your chin up". Pointing this out, as the forum is international and some might mistake the expression as something less savory.

Oops. Yes, "chin" is better. I am sorry if I offended any Americans.

Boltzmann brain · 2020-02-11, 22:24

I understood the intention haha, the naughtier version did briefly come to mind though :P (I am from the UK)
Today I've started to try to resolve 22246 in chunks of 10M steps (takes about 3 hours atm). Currently doing 30-40M. At the 30M mark it was over 4200 digits...

Boltzmann brain · 2020-02-12, 20:38

30-40M and 40-50M took 8 and 9.5 hours respectively. It has also grown considerably in size. at 50 M it was 7809 digits in size, with a 8307 digit maximum in the 10M before. For a sequence that should always terminate, this is doing a very good job of not doing so... If there is anyone who is capable of helping, I would be grateful! If you wish, I can provide the 49,999,996th term (I included the input number as term 1, so when I re-input the result after 10M, the first term is counted twice as a result, so subtract the number of times I have done this). I would also be curious in what a plot of this would look like.

2020-02-10, 13:18	#12
LaurV Romulan Interpreter Jun 2011 Thailand 23·419 Posts	Moved to misc math. RDS is right, in spite of the fact that his "go back to the books" attitude is known here around, and so it is his sensitivity about what's posted in the Math subforum, and in spite of the fact that we consider his reaction a bit too exaggerated, it is misc math. Or it could be at best destined to the Puzzles thread (it actually can make a nice puzzle, and we'll like to play with it a little in the future... any takers?). The OP stated clearly this is recreational for him, and he doesn't want to break any math boundaries with it. Moreover, no claim of solving Collatz was made, in fact, the two problems are barely related. Yet, this may be a nice puzzle... Lack of knowledge does not make one stupid, and recognizing incompetence in a domain does not make one stupid, even if he wants or not to learn about. People have better thinks to do. I can't speak Japanese, and I don't want to learn it (well... I want, but I always find something better to do, and few trials in the past resulted in no progress, so I am still wondering if I am stupid or not... but don't tell that to these guys here...) Last fiddled with by LaurV on 2020-02-10 at 13:20

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2020-02-10, 16:24	#13
Boltzmann brain Feb 2020 11 Posts	Honestly, I'm a little surprised that the result of the operation is on average 0.75 the size of the input. I'd have thought it would be a bit narrower than that, especially considering the size of some of the resultant numbers. Then again, with a large enough sample such variance should turn up stuff like this every so often. I wonder what the chance is of a number ~20000 reaching 1600 digits in 10M operations when on average each step is 0.75 the previous. That may or may not be easy to calculate. Thanks for moving it LaurV, it does seem it would fit better here. I was disheartened by RDS's comments but I could understand where he was coming from. In truth, I did suffer minor traumatic flashes for the rest of the day but that's more a reflection of my fragile mental state (I have rather severe social anxiety, I am on medication so don't worry too much). At the moment, the puzzle seems to be: does 22246 terminate? This is reminding me of the aliquot sequence of 276, though without the factoring thank goodness!

2020-02-11, 22:24	#17
Boltzmann brain Feb 2020 11 Posts	I understood the intention haha, the naughtier version did briefly come to mind though :P (I am from the UK) Today I've started to try to resolve 22246 in chunks of 10M steps (takes about 3 hours atm). Currently doing 30-40M. At the 30M mark it was over 4200 digits...

2020-02-12, 20:38	#18
Boltzmann brain Feb 2020 11 Posts	30-40M and 40-50M took 8 and 9.5 hours respectively. It has also grown considerably in size. at 50 M it was 7809 digits in size, with a 8307 digit maximum in the 10M before. For a sequence that should always terminate, this is doing a very good job of not doing so... If there is anyone who is capable of helping, I would be grateful! If you wish, I can provide the 49,999,996th term (I included the input number as term 1, so when I re-input the result after 10M, the first term is counted twice as a result, so subtract the number of times I have done this). I would also be curious in what a plot of this would look like.