King of Herdaz

Anyone in the mood of a number puzzle

15 posts in this topic

I came up with this sequence in math class a couple of months ago when we were asked to make up a rule, write down a sequence using that rule, and pass them around the room. When you figured out the rule you were supposed to trade with someone else and try to figure out that one. Afterwards the professor put the sequences that stumped people on the board and we figured them out together. However the following sequence which I made wasn't solved and stumped the whole class, professor included. So here it is:

0,0,3,16,45,120,280,624,1323,2720...

Try to figure the rule for this sequence.

Edited by King of Herdaz
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Just saying, this is nearly impossible. Here is another one!

1, 1, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0...

GL!

Can we limit it down to simple functions, or not? (for the first one)

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If you want a hint:

Spoiler

it is two sequences multiplied together. the first term in both sequences is 0

 

Edited by King of Herdaz
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41 minutes ago, GoWibble said:

Just saying, this is nearly impossible. Here is another one!

1, 1, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0...

GL!

Can we limit it down to simple functions, or not? (for the first one)

Does it ever change from zero after the first 4 terms??

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nope

:D

though I didn't go to infinity...

oh, and the first one is the 0th one

and your magic number is 2

Edited by GoWibble
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36 minutes ago, GoWibble said:

and your magic number is 2

What do you mean?

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It has a 2 in the equation. 

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@King of Herdaz is the answer

Spoiler

The Fibonacci sequence multiplied by the multiple of successive integers separated by two? So

  • 0, 1, 1, 2, 3, 5, 8, 13, 21, 34
    • (0, 1, (0+1 = 1), (1+1 = 2), (1+2 = 3), (2+3 = 5), ... N(m-2)+N(m-1) = N(m))
  • 0, 0, 3, 8, 15, 24, 35, 48, 63, 80
    • (0, 0, (1*3), (2*4), (3*5), (4*6), ... N(y)*N(y+2) = N(z))

 

Can you answer this one?

2, 72, 5184, 640000, 121500000, 32934190464, 12089663946752, ...

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On 12/20/2019 at 2:21 PM, Ixthos said:

@King of Herdaz is the answer

  Hide contents

The Fibonacci sequence multiplied by the multiple of successive integers separated by two? So

  • 0, 1, 1, 2, 3, 5, 8, 13, 21, 34
    • (0, 1, (0+1 = 1), (1+1 = 2), (1+2 = 3), (2+3 = 5), ... N(m-2)+N(m-1) = N(m))
  • 0, 0, 3, 8, 15, 24, 35, 48, 63, 80
    • (0, 0, (1*3), (2*4), (3*5), (4*6), ... N(y)*N(y+2) = N(z))

 

Spoiler

you got the first part right, and while i used (n^2)-1, what you gave for the second part also works. good job!

 

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On 12/22/2019 at 2:56 AM, King of Herdaz said:
  Hide contents

you got the first part right, and while i used (n^2)-1, what you gave for the second part also works. good job!

 

Spoiler

Makes sense. (n-1)(n+1) = n^2 - n + n - 1 = n^2 - 1

:-)

 

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On 12/20/2019 at 11:21 AM, Ixthos said:

@King of Herdaz is the answer

  Reveal hidden contents

The Fibonacci sequence multiplied by the multiple of successive integers separated by two? So

  • 0, 1, 1, 2, 3, 5, 8, 13, 21, 34
    • (0, 1, (0+1 = 1), (1+1 = 2), (1+2 = 3), (2+3 = 5), ... N(m-2)+N(m-1) = N(m))
  • 0, 0, 3, 8, 15, 24, 35, 48, 63, 80
    • (0, 0, (1*3), (2*4), (3*5), (4*6), ... N(y)*N(y+2) = N(z))

 

Can you answer this one?

2, 72, 5184, 640000, 121500000, 32934190464, 12089663946752, ...

Yeah.

...The OEIS is a very powerful tool :D

Edited by Ammon Kunzler
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8 hours ago, Ammon Kunzler said:

Yeah.

...The OEIS is a very powerful tool :D

Cheater :-P :-D

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Heres another

0,1,8,3,20,45,12,42,40,27,50,88,108,91,126,45,32,51,144,76,120...

Quick warning: it is pretty irrational and counter-intuitive, though not too complicated.

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@Ammonakin 

Spoiler

Hmmm ... so far, just looking at it, I see that the zeroth entry is zero, the first is 1*1, the second is 2*4, the third is 3*1, the fifth is 5*4, the sixth is 6*2, the seventh is 7*6, the eighth is 8*5, the ninth is 9*3, the tenth is 10*5, the eleventh is 11*8, ... and so making a list of the number unlike its place, we get the sequence of 1, 4, 1, 5, 9, ... which makes me wonder if the first number - the multiple for zero - was a three.

 

Fancy some pi? ;-)

Edited by Ixthos
Forgot to put this in spoilers!
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