A354266 Pairs of integers (s, t) such that 0 < s < t and gcd(s, t) > 1, where the pairs are generated by the boustrophedonic Cantor enumeration A319571.

2, 4, 2, 6, 3, 6, 2, 8, 4, 6, 2, 10, 3, 9, 4, 8, 2, 12, 4, 10, 6, 8, 3, 12, 5, 10, 6, 9, 2, 14, 4, 12, 6, 10, 2, 16, 3, 15, 4, 14, 6, 12, 8, 10, 2, 18, 4, 16, 5, 15, 6, 14, 8, 12, 3, 18, 6, 15, 7, 14, 9, 12, 2, 20, 4, 18, 6, 16, 8, 14, 10, 12, 2, 22, 3, 21

Offset

1,1

Links

Table of n, a(n) for n=1..76.

Example

The sequence of pairs starts:
(2, 4), (2, 6), (3, 6), (2, 8), (4, 6), (2, 10), (3, 9), (4, 8), (2, 12), (4, 10),(6, 8), (3, 12), (5, 10), (6, 9), (2, 14), (4, 12), (6, 10), (2, 16), (3, 15),(4, 14), (6, 12), (8, 10), ...

Prog

(Julia)
function A354266List(upto)
    L = Int[]
    for n in 1:upto
        d = div(isqrt(8n + 1) - 1, 2)
        s = n - div(d*(d + 1), 2)
        t = d - s
        if s > 0 && s < t && gcd(s, t) > 1
            push!(L, s)
            push!(L, t)
        end
    end
L end
println(A354266List(303))

Crossrefs

Cf. A319571.

Sequence in context: A230436 A105393 A182812 * A360005 A360457 A328985

Adjacent sequences: A354263 A354264 A354265 * A354267 A354268 A354269

Keyword

nonn

Author

Peter Luschny, May 21 2022

Status

approved