Goahead52's Math Posts

For the discussion of math. Duh.

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Goahead52
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Re: Goahead52's Math Posts

Postby Goahead52 » Thu Aug 25, 2016 7:52 pm UTC

Alexandre Grothendieck is surely not known to Lorb.
I expected it.

JudeMorrigan
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Re: Goahead52's Math Posts

Postby JudeMorrigan » Thu Aug 25, 2016 8:01 pm UTC

Soupspoon wrote:
Goahead52 wrote:I`m honored to be called imposter because all the Prophets : Moses, Jesus, Muhammad and others were labelled as imposters. Galilee was called imposter and decapitated.

Beware the Galileo Gambit...

And while it's by far the lesser issue, I'll add that Galileo was not decapitated.

Goahead52
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Re: Goahead52's Math Posts

Postby Goahead52 » Thu Aug 25, 2016 8:03 pm UTC

Soupspoon wrote:
Goahead52 wrote:I`m honored to be called imposter because all the Prophets : Moses, Jesus, Muhammad and others were labelled as imposters. Galilee was called imposter and decapitated.

Beware the Galileo Gambit...

It was Copernic who was decapitated not Galileo.
ha ha ha
Copernic Gambit?
bye bye
I will never ever post here.

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Re: Goahead52's Math Posts

Postby Newt » Thu Aug 25, 2016 8:20 pm UTC

It might be time to follow the corollary to 'don't feed the troll', 'don't turn the crank'.

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Re: Goahead52's Math Posts

Postby Soupspoon » Thu Aug 25, 2016 9:27 pm UTC

JudeMorrigan wrote:
Soupspoon wrote:
Goahead52 wrote:I`m honored to be called imposter because all the Prophets : Moses, Jesus, Muhammad and others were labelled as imposters. Galilee was called imposter and decapitated.

Beware the Galileo Gambit...

And while it's by far the lesser issue, I'll add that Galileo was not decapitated.

I nearly said that. He wrote "Galilee", which, in that context and select company, presumes some biblical figure. Perhaps even John The Baptist, like "The Nazareen" might have been used for his contempoary. But my misreading it at first directly reminded me of the Gambit and it started off as "Oh look, an actual example of...", even.

(To be honest, it had been looking like the 'conversation' had been going that way for a while... I had been tempted to quote Jimmy Durante: "People said I was mad. but that didn't trouble me. They said Mozart was mad. They said Puccini was mad. They said Louis was mad. Who's Louis? My uncle. He was mad!")

Copernicus died of natural/age-and-illness-related causes, as with Galileo, near as we can know for sure. Can't think of a beheaded scientist, of their ilk. Another reason I think that I just don't understand Goahead's actually intended reference, and now never will if he is now quit. Never mind. I'll survive, and I'll hope everyone else does too.

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Re: Goahead52's Math Posts

Postby doogly » Thu Aug 25, 2016 11:38 pm UTC

Archimedes, maybe?
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Re: Goahead52's Math Posts

Postby lorb » Fri Aug 26, 2016 7:48 am UTC

Antoine Lavoisier was beheaded, but same as Archimedes, it was because of the political circumstances and had nothing to do with them being scientists.
Please be gracious in judging my english. (I am not a native speaker/writer.)
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Re: Goahead52's Math Posts

Postby PM 2Ring » Sat Aug 27, 2016 6:04 pm UTC

The philosopher / mathematician / poet Giordano Bruno, who promoted & extended the Copernican theory, was burned at the stake.

Goahead52
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Re: Goahead52's Math Posts

Postby Goahead52 » Sun Aug 28, 2016 10:58 am UTC

(7-1)+(7-1)*(7^2)*(1+7+7^2+...+7^k) is always a triangular number for any k

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Re: Goahead52's Math Posts

Postby jaap » Sun Aug 28, 2016 1:05 pm UTC

Goahead52 wrote:(7-1)+(7-1)*(7^2)*(1+7+7^2+...+7^k) is always a triangular number for any k

k=0:
(7-1)+(7-1)*(7^2)*(7^0) = 300 = 24*25/2 = Triangle(24)

k=1:
(7-1)+(7-1)*(7^2)*(7^0+7^1) = 2358 is not triangular. Triangle(68) = 2346, Triangle(69) = 2415

k=2:
(7-1)+(7-1)*(7^2)*(7^0+7^1+7^2) = 16764 is not triangular. Triangle(182) = 16653, Triangle(183) = 16836

k=3: 117606 is not triangular
k=4: 823500 is not triangular
k=5: 5764758 is not triangular
k=6: 40353564 is not triangular
k=7: 282475206 is not triangular
k=8: 1977326700 is not triangular
k=9: 13841287158 is not triangular

Goahead52
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Re: Goahead52's Math Posts

Postby Goahead52 » Sun Aug 28, 2016 1:14 pm UTC

Thank you for your correction.
I did maybe some mistake in my formula.
I will correct it soon.
In my Excel all is fine.
The final formulation is fo sure wrong as you pointed it out.

Goahead52
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Re: Goahead52's Math Posts

Postby Goahead52 » Sun Aug 28, 2016 2:01 pm UTC

Here are my results on Excel :
3 9 2 18 18 6 12 3 12
21 441 2 882 900 300 600 24 600
147 21609 2 43218 44118 14706 29412 171 29412
1029 1058841 2 2117682 2161800 720600 1441200 1200 1441200
7203 51883209 2 103766418 105928218 35309406 70618812 8403 70618812
50421 2542277241 2 5084554482 5190482700 1730160900 3460321800 58824 3460321800

The last 3 colums check if it is a triangular number or no.
How I reached my formula (wrong formulation)?
By starting to sum the multiples of 3.
I have found a serie summing 3*T(n)
I did some mistake by trying to simplify the formula.
I will fix it but not now.
I gave you the brute results.
It is easy to retrieve the formulas entered in cells.
Very sorry.
You have to copy paste the results above in Excel to have a clear grid 9 columns x 6 rows.

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Re: Goahead52's Math Posts

Postby jaap » Sun Aug 28, 2016 3:41 pm UTC

The formula you found should be:
(7-1)*(1+72+74+...+72k) is always a triangular number for any k

This is true, because:
Spoiler:
Using the formula for summing geometric series, this number is
S = (7-1)*(1+72+74+...+72k)
= 6*(72(k+1)-1)/(72-1)
= 6*(72(k+1)-1)/48
= (72(k+1)-1)/8

S is a triangular number, because 8S+1 is a square:
8S+1 = 72(k+1) = (7(k+1))2
so S is the triangular number Triangle(7(k+1)).


Edit: More generally, if b=2c+1 is any odd number, then
Triangle(c) * (1 + b^2 + b^4 + ... b^2k ) is always a triangular number for any k.

Goahead52
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Re: Goahead52's Math Posts

Postby Goahead52 » Sun Aug 28, 2016 4:20 pm UTC

Thank you very much for correcting me.
My results on Excel were correct. I failed to express it as you did.
I have many others equivalent to T(n) to sum of squares (1,4,9,16.....).
I need to check and recheck them all.
Someone send me my algorithm (I have posted it in a french forum) written in python.
It is a new way of summing sequences (any sequence could have a solution even the sequence of prime numbers or the Euler totient`s ).

Big thanks! I go back to the development of my new ideas.

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Re: Goahead52's Math Posts

Postby Goahead52 » Tue Aug 30, 2016 1:15 am UTC

Today while working on inverted Eratosthenes sieve (we start from the last prime and we decrease our counter to reach 2 instead of starting with 2,3,5,7....) I made a huge discovery : a prime counting function giving the exact pi(n) not an approximation.
Anyway as I make many mistakes (lack of focus) I need the help of one of you who is tooled (programming and arithmetic field) to help me present my algorithm. I almost finished writing it in french.
It will work like this :
For counting the primes between 2 and p^2 we need to have the primes from 2 to p.
We do not need to use the Eratosthenes sieve.
To each prime from is associated a function with one parameter v(p).
We just sum all the v(p) from 2 to p and we have directly our pi(p^2).
v(p) is pre computed for all the p`s we want. If we have the first 10^12 p`s each p have each v(p) associated with p.
We need to store the v(p) once computed. Each v(p) use the algorithm for cycle detection. I will give more details with p=97 and p^2=9409 on how to compute v(p).
The advantage of my method is that the v(p)`s could be computed independently which open the path for massive parallel programming.
I will give more details once I finish the translation in English.
I will publish it here.

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Re: Goahead52's Math Posts

Postby Cauchy » Tue Aug 30, 2016 7:54 am UTC

If you have to consult a lookup table, why not just store the number of primes itself? That way, you don't have to do any summation after you look up numbers.
(∫|p|2)(∫|q|2) ≥ (∫|pq|)2
Thanks, skeptical scientist, for knowing symbols and giving them to me.

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Re: Goahead52's Math Posts

Postby Goahead52 » Tue Aug 30, 2016 10:15 am UTC

Cauchy wrote:If you have to consult a lookup table, why not just store the number of primes itself? That way, you don't have to do any summation after you look up numbers.

What you say is correct but if ( I still do not know) there is a way to find closed formula for the v(p) then pi(n) will be more even with n large.
Finding a cycle for each p was maybe solved in mathematical litterature.
One question before : is there a formula or an algorithm to find the multiples of p not divided by primes less than or equal p.

P=11
multiples of p
11,22,33,44,55,...121......
22 is divided by 2 < 11 then removed
33 the same etc...
but 121 will be on the list (because = 11*11). All the divisors are >=11

143 is on the list = 11*13
If this problem was solved then I will be very happy.

Thank you for your comments.

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Re: Goahead52's Math Posts

Postby Goahead52 » Tue Aug 30, 2016 10:46 am UTC

Here is a table of v(p)`s for the first 25 primes :
First column the first 25 primes
Second the values of v(p) for the range of numbers from 2 to 10200
2 5100
3 1700
5 680
7 389
11 212
13 162
17 114
19 96
23 79
29 62
31 57
37 48
41 42
43 39
47 34
53 29
59 24
61 23
67 19
71 16
73 15
79 11
83 9
89 8
97 4

The meaning of each line is that for any p of the list v(p) is equal to all the multiples of p not divided by primes less than p

p=29 v(p)=62 means that there 62 numbers multiples of 29 and NOT DIVIDED by 2,3,5,7,....,23.
v(p) is the result of computation not a program.
Do we know how to compute v(p)?
I searched on internet and I did not find any document refering to such problem.
Thank you for any help.
Maybe I did reinvent the wheel.

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Re: Goahead52's Math Posts

Postby Demki » Tue Aug 30, 2016 11:14 am UTC

There are infinitely many multiples of 29 not divisible by primes less than 29. A subset of these multiples is {29^k | k∈N\{0} } and that subset is countably infinite.

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Re: Goahead52's Math Posts

Postby Goahead52 » Tue Aug 30, 2016 11:26 am UTC

Demki wrote:There are infinitely many multiples of 29 not divisible by primes less than 29. A subset of these multiples is {29^k | k∈N\{0} } and that subset is countably infinite.

Yes, I agree with you but here I`m talking about a finite range 2 to 10200.
Is there a way to know how many without listing the multiple and removing those not divided par less than p (here in my example 29)?

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Re: Goahead52's Math Posts

Postby Demki » Tue Aug 30, 2016 11:32 am UTC

None that I know.

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Re: Goahead52's Math Posts

Postby Goahead52 » Tue Aug 30, 2016 11:52 am UTC

Demki wrote:None that I know.

Thank you.
f we sum the v(p)=8972 and we substract the first 25 primes we will obtain : 8947 which is exactly the number of composites numbers between 1 and 10200. Henece the number of primes will be 10200-8947=1252 primes.
I know how to calculate once for all the values of v(p)`s.
We have more accurate prime counting function.
Is it practical when n get bigger? I do not know.
Is it of theoretical interest? I do not know
Can we improve my method and find links to other NT problems? For sure we can.
Is my method new? I do not know

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Re: Goahead52's Math Posts

Postby Goahead52 » Wed Aug 31, 2016 11:05 am UTC

I removed my post.
I`m very tired so I quit internet once for all.
I need to take vacations for the rest of my life.
Good luck to everybody.

Goahead52
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Counting functions : perfect powers and semiprimes

Postby Goahead52 » Sun Sep 11, 2016 12:32 pm UTC

Hi,

Internet is very addictive.
I finally succeded to find 2 formulas :
1. Counting the perfect powers
2. Counting the semiprimes

As I do not know how to use Latex here I send 2 picrures of the 2 formulas here :

http://hpics.li/30e2b69

http://hpics.li/ab9d8ae

If one of you who masters Latex can reproduce my formulas here in this forum it will stay here in the forum forever otherwise hostinpics site will remove them after some period of time.

Thank you.

I`m waiting your comments anyway.

Goahead52
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Re: Goahead52's Math Posts

Postby Goahead52 » Mon Sep 12, 2016 12:07 am UTC

To be honest and not hypocrite the moderator has to call it Goahead52`s math garbage instead of Goahead52`s math posts.
It is a lack of respect toward me and toward those searching for some subject in particular.
As you are the captain on board you have what I call in french a huge disease "la dictaturite"

NOW FUCK YOU YOU CAN BANISH ME FROM NOW.

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Re: Goahead52's Math Posts

Postby gmalivuk » Mon Sep 12, 2016 12:15 am UTC

Everything is just as searchable as it ever was, because I didn't delete any text (either from the post subject or the post itself) when I merged the threads.

But you're welcome to quit (again) if it makes you feel better.
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Re: Goahead52's Math Posts

Postby Demki » Mon Sep 12, 2016 5:13 am UTC

Goahead, the thing is that all your posts are about number theory, so there's no real "searching for subject"
And we can search post text too.

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Re: Goahead52's Math Posts

Postby Goahead52 » Mon Sep 12, 2016 9:25 pm UTC

Anyway the moderator is the God on his forum.
But I`m the God for publishing or not my formulas.
Today I have finished my formula counting the exact number of prime less than n
Good luck to you.
Now I can rest and cut off internet once for all.
No phone no internet no tv
Drinking fucking eating reading and that`s it.

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Re: Goahead52's Math Posts

Postby gmalivuk » Tue Sep 13, 2016 1:30 am UTC

Sounds like a nice life.

Enjoy.
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