[grey cells]

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

[grey cells]

Folks , try arriving at the explanation . I will post the explanation after 15 days , i.e. , if nobody's already found the explanation by then( I will not be logging in until then.)

So goodbye .

[Guest]

Ok I read through this thread last night before I went to bed. It kept me up 3 hours past my bedtime.

I thought I had it figured out just looking at the binary.

2 00000010 1

5 00000101 2

11 00001011 3

17 00010001 2

137 10001001 3

149 10010101 4

173 10101101 5

It looked to me like there was a pattern, 2 1s, 3 1s, 2, 3, 4, 5

But then I wrote all the prime numbers up to 200 in binary.

The number to the right is how many "1"s there are. The *special* numbers are marked.

2 00000010 1

3 00000011 2

5 00000101 2

7 00000111 3

11 00001011 3

17 00010001 2

19 00010011 3

23 00010111 4

29 00011101 4

31 00011111 5

37 00100101 3

41 00101001 3

43 00101011 4

47 00101111 5

53 00110101 4

59 00111011 5

61 00111101 5

67 01000011 3

71 01000111 4

73 01001001 3

79 01001111 5

83 01010011 4

89 01011001 4

97 01100001 3

101 01100101 4

103 01100111 5

107 01101011 5

109 01101101 5

113 01110001 4

127 01111111 7

131 10000011 3

137 10001001 3

139 10001011 4

149 10010101 4

151 10010111 5

157 10011101 5

163 10100011 4

167 10100111 5

173 10101101 5

You can see that the pattern of 2, 3, 2, 3, 4, 5 doesn't really fit when you look at all the primes.

That made me think that perhaps he was just adding an extra digit to the end.

2 10

5 101 added a 1

11 1011 added a 1

17 10001 ???

137 10001001 added 001

149 10010101 ???

173 10101101 ???

From your other clues, where you mentioned bases, that made me think maybe the numbers written in another base were prime.

Written in binary, only 5 was still primary (101), but...

Written in base 4 (which isn't used for anything other that me stretching to find a pattern here). I tried using other bases (8 or 16 for example, but they didn't make it this far)

2 2 Prime

5 11 Prime

11 23 Prime

17 101 Prime

137 2021 Not Prime

149 2111 Prime

173 2231 Not Prime

That didn't work, obviously

So I'm still stumped. But I'm going to continue thinking about this. <_<

[grey cells]

MLeww , good tries . But don't lose your sleep over this .

I will give you a hint.

See post#75 , in the same page , carefully and I am sure you will get it.

And I will not be logging in for the next 10 days . But feel free to post your explanation.

[Guest]

Because you haven't shown it repeating then pretty much anything could fit, ie it might be +3 +6 +22 +104?

But I'll go with 53: 2 5 11 53 137 725.

+3 +6 +42(6*7) +84(42*2) +588(84*7)

[grey cells]

Because you haven't shown it repeating then pretty much anything could fit, ie it might be +3 +6 +22 +104?

But I'll go with 53: 2 5 11 53 137 725.

+3 +6 +42(6*7) +84(42*2) +588(84*7)

Hex Raikou , Welcome to the den !.

good one there .

But I have given the hint as "play with the bases".

And the next 2 numbers are 149 and 173.

[Guest]

Hex Raikou , Welcome to the den !.

good one there .

But I have given the hint as "play with the bases".

And the next 2 numbers are 149 and 173.

Thanks for the welcome, but I only saw the hint afterwards, Hmm, Then its +3 +6 +? +? +12 +24, I'll think about it and post ;ater, this'll be used to help others.

[grey cells]

Thanks for the welcome, but I only saw the hint afterwards, Hmm, Then its +3 +6 +? +? +12 +24, I'll think about it and post ;ater, this'll be used to help others.

It does not have anything to do with Addition or any other arithmetic operation.

And use binary number system.

[Guest]

Are we finally going to get an explanation to your seemingly random choice of prime numbers. I've looked at the binary quite a bit, and can't seem to find a pattern of any sort.

[grey cells]

Are we finally going to get an explanation to your seemingly random choice of prime numbers. I've looked at the binary quite a bit, and can't seem to find a pattern of any sort.

The explanation will be certainly given , but not by me . I have posted the puzzle for you guys to solve , and hey they are not a seemingly random choice of prime numbers , they ARE a random choice of prime numbers .

Just kidding . Seriously , I would not waste the time of the folks on this forum . This is a genuine , non-replicated puzzle created by me .

[grey cells]

I have already given this hint , but I think it has somehow managed to lose itself in the den . Naughty , naughty hint .If somebody catches it prowling around , don't forget to give it a good spanking and please send it back to Papa puzzle.

HINT: Reverse the bits .

MOST IMPORTANT : The maximum number of bits used for Decimal numbers from 1 to 15 is four.(0000 to 1111) and for numbers from 16 to 255(0001 0000 to 1111 1111).

[Guest]

Ok grey cells, now that you posted more of a hint on your pattern, I have it figured out. I had tried reversing the bits, but I was writing 17 as a 6 bit number, instead of jumping to 8, and that was messing everything up quite a bit.

Just flip the binary around, and go to the next higher prime number. Make sure to use 4 bits for numbers 1 through 15, and 8 bits for numbers 16 through 255.

2 is 0010. Flip that and you have 0100, which is 4. The next higher prime is 5.

5 is 0101. Flip to 1010 which is 10, the next prime is 11.

11 is 1011. Flip that to 1101, which is 13. But following the 'next higher' pattern, 17 is next highest after 13.

17 = 00010001. Flip that to 10001000, which is 136. Next prime - 137.

137 = 10001001. Flip to 10010001, which is 145. The next prime is 149.

149 = 10010101. Flip that to 10101001, which is 169. The next prime is 173.

173 = 10101101. Flip that to 10110101, which is 181. The next prime is 191.

191 = 10111111. Flip that to 11111101, which is 253. The next prime is 257, and that takes us to another set of 4 bits. I don't feel like demonstrating any further than this. (2063, 3847, etc...)

I don't think this pattern could continue forever though. After 3847, it drops to 3607. But now that I finally get to post the solution, I'm content.

I also think that nobody actually solved for 17, we all just pretty much guessed until you told us it was 17.

Now it's cookie time.

[grey cells]

Hey ! MLeww well done . You have cracked it . But you get only half a cookie since you have arrived at the answer after a hint . But since you have put so much time into this one , maybe I can you give you one teeny-weeny cookie.

By the way , CIA are still working on it and they still haven't decoded it . Maybe you could provide them some valuable assistance.

And kudos to Nikyma for getting the answer.