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

mathaholic
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Registered: 2012-11-29
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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)


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

bobbym
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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.

If it ain't broke, fix it until it is.

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

mathaholic
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Re: Julianthemath's number 3

Oh.


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

bobbym
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Re: Julianthemath's number 3

48 is the next number.


In mathematics, you don't understand things. You just get used to them.

If it ain't broke, fix it until it is.

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

mathaholic
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Re: Julianthemath's number 3

Good. Next pattern soon!


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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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Re: Julianthemath's number 3

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


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

berliner
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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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Re: Julianthemath's number 3

In the OEIS again. sad


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

berliner
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Re: Julianthemath's number 3

It's one of my sequence


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

anonimnystefy
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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
The knowledge of some things as a function of age is a delta function.

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

bobbym
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Re: Julianthemath's number 3

Did you check the OEIS?


In mathematics, you don't understand things. You just get used to them.

If it ain't broke, fix it until it is.

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

anonimnystefy
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From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

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
The knowledge of some things as a function of age is a delta function.

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

bobbym
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From: Bumpkinland
Registered: 2009-04-12
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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.

If it ain't broke, fix it until it is.

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

anonimnystefy
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From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

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
The knowledge of some things as a function of age is a delta function.

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

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 97,283

Re: Julianthemath's number 3

Okay, thanks for the help.


In mathematics, you don't understand things. You just get used to them.

If it ain't broke, fix it until it is.

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

anonimnystefy
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From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

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
The knowledge of some things as a function of age is a delta function.

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

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 97,283

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.

If it ain't broke, fix it until it is.

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

anonimnystefy
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From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

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
The knowledge of some things as a function of age is a delta function.

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

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 97,283

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.

If it ain't broke, fix it until it is.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

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
The knowledge of some things as a function of age is a delta function.

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 97,283

Re: Julianthemath's number 3

The tensor operator does what here?


In mathematics, you don't understand things. You just get used to them.

If it ain't broke, fix it until it is.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

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
The knowledge of some things as a function of age is a delta function.

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

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 97,283

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.

If it ain't broke, fix it until it is.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

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
The knowledge of some things as a function of age is a delta function.

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