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2

This can be considered as a kind of covering problem, which can be formulated as an integer linear programming problem. Suppose you want to see if $A144311(n) \ge m$. We ask to cover the set $S = \{1, \ldots, m\}$, where each prime $p$ of the first $n$ primes will cover those members of $S$ congruent to $a_p \pm 1 \mod p$ for some $a_p \in \{0, \ldots, ...


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Taking @joriki's approach, I've now written a version that runs in Mathematica. I'm including now only the latest and just previous revisions to keep this from getting lengthy. The last revision saw a 5x speedup do to the number between twin primes being divisible by 6, and (in the case of my code) the number $2$ and $4$ more than the twins respectively ...


3

I see basically two approaches, and a hybrid of them that's more efficient than either. First, you could try out all combinations of residues other than $-1,1$ that the primes could have at the one end of the sequence, and then see how far you get in each case. The number of combinations would be $$ \prod_{i=3}^n(p_i-2)\;, $$ i.e. ...


0

The covariance is $s_{xy} = \frac{\sum (x_i - \bar x)(y_i - \bar y)}{n-1},$ where the sum is taken over $i = 1, \dots, n$ and $n$ is the sample size. Then the correlation is $r_{xy} = \frac{s_{x,y}}{s_x s_y},$ where $s_x$ and $x_y$ are the two standard deviations. If you have the regression line y = 13.555 -0.1688842 x. then you might say (over the ...



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