prog theory: non/+coprime squares

Any two consecutive numbers, n and n+1, are co-prime
n and n+2 will have a gcd of at most 2, and n/2 and (n+2)/2 are coprime if integer

n and n+x will have a gcd of at most x, or will be factors of x, n/x and (n+x)/x are coprime if integer, and [n/gcd(n,n+x) and n+x /gcd(n,n+x)]
[n/gcd(n,n+x) and n+x], [n and n+x /gcd(n,n+x)] are coprime or have a gcd <= gcd(n,n+x)

Is this some math anome shit again

mersenne my anus

It's a possible finite decompression sequence

If a pair of numbers aren't co-prime, then we can expand from (n, n+x) to (n, n+x, n/gcd, n+x/gcd) and then check if (n, n+x/gcd) or (n/gcd, n+x) arent co-prime pairs (two expansion directions)

Adding one number to the pair and making it a triplet (n, n+x, n+y) gives three initial pairs, three possible dividers and six possible initial expansion directions?

To construct a triplet that hits three expansion directions n times each, we choose a ?(co-)prime triplet (c, d, e) and set n = c^f*d^g, n+x = d^h*e^i, n+y = e^j*c^k
n1 = g/h or h/g, n2 i/j, n3 f/k, with remainderless division