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#1 2013-04-14 18:19:43

mathaholic
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From: Juliania
Registered: 2012-11-29
Posts: 2,845
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Julianthemath's number 3

This is my third version of the Julianthemath number (since Nehushtan got the rule of my sequence).

It is the sum of 2 consecutive square numbers, and 2 consecutive triangular numbers, minus the 2 square roots and 2 triangular roots. Here, for simplification :

S = Square
SR = Square Root
T = Triangular
TR = Triangular root

This is also called the : Squmintrius number (complex, right? smile)

Examples :
1. ( (1+4)-(1+2) ) + ( (1+3)-(1+2) )
( 5 - 3 ) + ( 4 - 3 )
2 + 1
3, a Squimintrius number

2. ( (4+9)-(2+3) ) + ( (3+6)-(2+3) )
( 13 - 5 ) + ( 9 - 5 )
8 + 4
12

3. ( (9+16)-(3+4) ) + ( (6+10)-(3+4) )
( 25 - 7 ) + ( 16 - 7 )
18 + 9
27

So, the Squimintrius sequence is : 3, 12, 27... So, what's the pattern here?

Last edited by julianthemath (2013-04-14 19:05:29)


"Double the fun, double the thrill, double the coolness" - Julianthewiki

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#2 2013-04-14 18:48:38

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,636

Re: Julianthemath's number 3

That second number should be 12 not 11.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2013-04-14 19:04:34

mathaholic
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From: Juliania
Registered: 2012-11-29
Posts: 2,845
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Re: Julianthemath's number 3

Oh.


"Double the fun, double the thrill, double the coolness" - Julianthewiki

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#4 2013-04-14 19:16:01

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,636

Re: Julianthemath's number 3

48 is the next number.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#5 2013-04-14 19:18:42

mathaholic
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From: Juliania
Registered: 2012-11-29
Posts: 2,845
Website

Re: Julianthemath's number 3

Good. Next pattern soon!


"Double the fun, double the thrill, double the coolness" - Julianthewiki

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#6 2013-04-14 20:10:24

berliner
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Registered: 2013-04-02
Posts: 69

Re: Julianthemath's number 3

How about this sequence:

-2, -1, 8, 31, 74, 143, 244, 383, 566, 799...

Guess the pattern.


Mathematichs is the queen of sciences - C. F. Gauss

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#7 2013-04-14 20:25:47

mathaholic
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From: Juliania
Registered: 2012-11-29
Posts: 2,845
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Re: Julianthemath's number 3

Don't know. Maybe you should post it in "Berliner's number 1", or something smile


"Double the fun, double the thrill, double the coolness" - Julianthewiki

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#8 2013-04-14 20:30:47

berliner
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Registered: 2013-04-02
Posts: 69

Re: Julianthemath's number 3

Thanks. By the way the formula was:

a(n) = n^3-2n^2-1


Mathematichs is the queen of sciences - C. F. Gauss

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#9 2013-04-14 21:23:36

mathaholic
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From: Juliania
Registered: 2012-11-29
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Re: Julianthemath's number 3

In the OEIS again. sad


"Double the fun, double the thrill, double the coolness" - Julianthewiki

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#10 2013-04-14 21:33:04

berliner
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Registered: 2013-04-02
Posts: 69

Re: Julianthemath's number 3

It's one of my sequence


Mathematichs is the queen of sciences - C. F. Gauss

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#11 2013-04-15 06:27:23

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Julianthemath's number 3

Continue this sequence and find the general form:
1,2,3,4,5,6,7,8,...


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#12 2013-04-15 06:58:05

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,636

Re: Julianthemath's number 3

Did you check the OEIS?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#13 2013-04-15 07:16:28

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Julianthemath's number 3

There are many possible answers that OEIS gives. But not all are the ones I am looking for.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#14 2013-04-15 07:19:30

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,636

Re: Julianthemath's number 3

It could be a new sequence. I would like very much to see a few more terms. Can you compute them?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#15 2013-04-15 07:33:36

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Julianthemath's number 3

I am sure it is not new.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#16 2013-04-15 07:39:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,636

Re: Julianthemath's number 3

Okay, thanks for the help.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#17 2013-04-15 07:49:48

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Julianthemath's number 3

This one:
1,5,4,22,26,86,...
on the other hand, is a new one. Or at least is not in the OEIS.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#18 2013-04-15 07:55:30

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,636

Re: Julianthemath's number 3

Hmmm, now you are talking. Let's have a few more of em and we are in business.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#19 2013-04-15 08:21:32

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Julianthemath's number 3

Do you want just the terms or the reccurence?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#20 2013-04-15 08:23:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,636

Re: Julianthemath's number 3

Hi;

The recurrence? Of course, provide it!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#21 2013-04-15 08:40:48

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Julianthemath's number 3

It is kinda unusual, though.

Last edited by anonimnystefy (2013-04-15 08:41:37)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#22 2013-04-15 08:47:31

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,636

Re: Julianthemath's number 3

The tensor operator does what here?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#23 2013-04-15 08:50:53

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Julianthemath's number 3

It represents the xor operation.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#24 2013-04-15 08:56:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,636

Re: Julianthemath's number 3

Okay, exclusive or. The next looks like a binary representation?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#25 2013-04-15 09:54:09

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Julianthemath's number 3

Yes, that is what it is.

You can replace it with this:

Last edited by anonimnystefy (2013-04-15 09:57:54)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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