BrainDen.com - Brain Teasers
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## Question

Try solving this number sequence:

One I made myself with my fav ingredients.

Find the missing number:

2 , 5 , 11 , _ , 137 ,.....

play with the bases

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Nikyma , You got it. Kudos to Nikyma.

The answer is 17 . But I am still waiting for the explanation.

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Nikyma , You got it. Kudos to Nikyma.

The answer is 17 . But I am still waiting for the explanation.

I'll let Noct know, I just didn't want you to be sad that everyone gave up

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I'll let Noct know, I just didn't want you to be sad that everyone gave up

Thanks for the encouragement and replies , Nikyma.

And thanks to the good ol' advice from LIS .

Still waiting for the explanation though.

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I'll tell you what my thinking was when I said 23.

2,5,11,__, 137

2+3=5, 5+6=11, 11+12=23, 23+24=47 (which, not understanding bases & binary, I assumed was equal to 137)

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For 17, I'd have to go with Noct on the "every other prime" idea. But, I don't understand the jump to 137?

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I'll tell you what my thinking was when I said 23.

2,5,11,__, 137

2+3=5, 5+6=11, 11+12=23, 23+24=47 (which, not understanding bases & binary, I assumed was equal to 137)

Good logical reasoning , Nikyma. But as you have said 47 is not 137.

EDIT : Just saw your other post .

If it was every other alternate prime number , it would have been too easy .

I hope now that the answer is known , someone will solve the reasoning part.

Edited by grey cells
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Waiting for the explanation. This one's easy . So I am not giving the explanation .

The answer is 17.(for those who don't want to go through previous posts).

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Waiting for the explanation. This one's easy . So I am not giving the explanation .

The answer is 17.(for those who don't want to go through previous posts).

Please post the next number in the sequence.

Let's see if someone gets the logic.

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Please post the next number in the sequence.

Let's see if someone gets the logic.

Seems like a good idea . OK here goes.

2 , 5 , 11 , 17 , 137 , 149 , 173 , ....

Hope now it is clearer.

In binary :

1=0001

Edited by grey cells
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Seems like a good idea . OK here goes.

2 , 5 , 11 , 17 , 137 , 149 , 173 , ....

Hope now it is clearer.

In binary :

1=0001

Lets wait and watch

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I did notice one thing, and I think I'm on the right track, but not all the way there yet.

If you list the numbers in order like this....

2

5

11

17

137

149

173

but in binary, they make this...

00000010

00000101

00001011

00010001

10001001

10010101

10101101

From this you can notice that each line is only different from it's previous line by exactly 3 digits every time. I guess the pattern would then be to change 3 digits and still be prime. If this rule sticks, I think it means the next number would be 197.

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I did notice one thing, and I think I'm on the right track, but not all the way there yet.

If you list the numbers in order like this....

2

5

11

17

137

149

173

but in binary, they make this...

00000010

00000101

00001011

00010001

10001001

10010101

10101101

From this you can notice that each line is only different from it's previous line by exactly 3 digits every time. I guess the pattern would then be to change 3 digits and still be prime. If this rule sticks, I think it means the next number would be 197.

observation , AI . It definitely looks that way .

But the next number , according to my reasoning is incidently not 197.

But your representation of 8 bits is spot-on.

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observation , AI . It definitely looks that way .

But the next number , according to my reasoning is incidently not 197.

But your representation of 8 bits is spot-on.

Is it higher or lower than 197?

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Is it higher or lower than 197?

Lower than 197 . And another hint is no need for any binary operations , not even binary addition , sub.

That's why I said it was easy.

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144

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I thought you said that this sequence combined two of your favourite things; prime numbers and binary.

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I thought you said that this sequence combined two of your favourite things; prime numbers and binary.

Yes , it definitely does.

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144

Nope .

is not 144.

If you have an explanation please post it.

Edited by grey cells
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OK . Good night guys . Believe me , the explanation is very easy.

Now off to bed (1:00 AM local time).ZZZZZZ.....

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177, 10110001

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144

The number must be prime.

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177, 10110001

He is not asking the next number, but the logic behind the sequence.

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177, 10110001

Sorry , It isn't 177 .

And the sequence does not involve any binary calculation . Just plain binary numbers.

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He is not asking the next number, but the logic behind the sequence.

Yes , you are right . But if someone comes at the right answer , then they must know the reasoning behind it.

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I did notice one thing, and I think I'm on the right track, but not all the way there yet.

If you list the numbers in order like this....

2

5

11

17

137

149

173

but in binary, they make this...

00000010

00000101

00001011

00010001

10001001

10010101

10101101

From this you can notice that each line is only different from it's previous line by exactly 3 digits every time. I guess the pattern would then be to change 3 digits and still be prime. If this rule sticks, I think it means the next number would be 197.

am sorry that I didn't mention this in my previous posts . But I think it is almost a giveaway to the reasoning . But to be fair to you all ,I will give a hint .

Now for the first 16 dec. numbers from 0 to 15 , the maximum number of bits used is 4 . So leave it at that.

For the numbers after 15 , obviously the number of bits used are more than 4 . So for only these numbers , we have to use AI's representation .

Sorry AI , I didn't say this beforehand . But as I have mentioned , this is a big hint.

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