Can you unlock this pattern? n°7.

The difference between each terms in this sequence is $8, 7, 5, 3, 9, 7, 3, 1, 7, 1$ This looks like the 10's complement of final digit of the n-th prime, that is: $10-\text{last digit of }n\text{-th prime.}$ Thus the next term in that particular sequence is $9$ , which means that the next number in our first sequence is: $51+9=60$ .

I would say the author is very good at linear regressions or at least a great coincidence of luck as he didn't take 59 as an answer. I wanted to guess him but I have chosen my own best answer namely 60. I prepared to guess his answer for several times namely 60, 59 and 56 in a sequence because the continuation of this sequence may not arise from linear regression but arise from something else. Yet, 60 has been the first correct guess!

Here are 3 linear regressions with x y-balanced, x's and y's respectively:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11

1   9.637762405 10.18181818 9.615782984 8
2   14.6738152  15.0969697  14.6567201  15
3   19.709868   20.01212121 19.69765721 20
4   24.7459208  24.92727273 24.73859433 23
5   29.7819736  29.84242424 29.77953144 32
6   34.8180264  34.75757576 34.82046856 39
7   39.8540792  39.67272727 39.86140567 42
8   44.890132   44.58787879 44.90234279 43
9   49.9261848  49.5030303  49.9432799  50
10  54.9622376  54.41818182 54.98421702 51
11  59.99829039 59.33333333 60.02515413 

This answer is a result of x y-balanced regression or an average of 3 linear regressions to me. I noticed 7, 5, 3, 9, 7, 3, 1, 7, 1 at first for a possible 9 next, but I didn't believe in this way.

Answer: $\boxed{60}$