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18

So the answer is I am not sure I have found the intended "key" and generating method, but one possible method is the following.


10

It's or or or or or


7

The odd one out is the This is because Safe Cracked!


7

The answer is: Because


6

I think the answer is: I found that the sequence has the following property: Here is a demonstration (not quite a proof, but convincing enough) that the property holds, and how I got the next numbers in the sequence:


5

So stacking Then the rest So So the four numbers are


5

My thoughts here are ... Why this sequence? Huh?


5

The answer is Obtained by Can obtained too through


5

Edit: (Old answer removed, apparently it was confusing the issue)


5

The oddball is because But


4

It appears that Note that So then


4

I've exhausted my mental state on this one today; my only plausible guess is: Because:


4

The nth element of the sequence is Alternatively, if you use an offset such that the first term has n=2, you could say Source for the second solution: https://oeis.org/A258107


4

Jaap Scherpuis found the answer, but the OP wants more explanation and a simple construction... I am middle aged bike rider still in prime shape. I have twin like older brother who is couple of years older than me. We both are cryptographers who love to play with fractions and our digital signatures consisting of long sequences that are closely tied to ...


4

First, I define three functions: Those functions produce the values Then we can express the sequence like that: Giving and finally so the next element is


4

Well, it is which so the answer is


4

Obviously the answer is because That is, For odd: $3/2 \times 1/2 = 3/4.$ $3/4 \times 1/2 = 3/8.$ For even: $2/3 \times 1/2 = 2/6\implies 1/3.$ $1/3 \times 1/2 = 1/6.$


4

The answer is You can generate this by


3

I will guess that it is My reasoning is that


3

My answer: Below is Meant as comment, but alas @John S posted the following in a comment at https://puzzling.stackexchange.com/a/83526/60039 It is missing data. However: Also:


3

The missing numbers are To find them, observe that


3

Well, let me try... So, the next one should be...


3

Answer: Explanation: etc. Note


3

The final grid is And the pattern is


3

Surely not the intended answer Jaap has of course identified the intended sequence. It seems to me that all the algorithms described so far are strictly more complicated than the following, which is simply another way of formulating the division operation and seems entirely straightforward to do in one's head. However, it can't be the intended answer ...


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