A366674 A366428 corresponding values for min(u, v) of Pythagorean triples (u, v, w) for which (u^2, v^2, w^2) is an "abc-hit".

7, 9, 16, 44, 17, 161, 175, 135, 297, 336, 52, 41, 116, 64, 49, 57, 720, 63, 276, 828, 96, 825, 237, 81, 1377, 1320, 128, 2016, 2080, 97, 3367, 99, 495, 721, 160, 1296, 164, 117, 5184, 125, 375, 127, 3375, 959, 824, 2793, 785, 2016, 161, 1183, 968, 492, 10296, 1000

Offset

1,1

Links

Felix Huber, Table of n, a(n) for n = 1..1420

Formula

a(n) = A366428(n)^2 - A366675(n)^2.

Example

A366428(1) = 25, the corresponding primitive Pythagorean triple is (7, 24, 25). a(1) = min(7, 24) = 7.

Maple

A366674:=proc(N) # To get all terms for which c <= N
    local a, b, c, i, l, p, q;
    l:=[];
    for p from 2 to floor(sqrt(N-1)) do
        for q to min(p-1, floor(sqrt(N-p^2))) do
            if gcd(p, q)=1 and is(p-q, odd) then
                c:=p^2+q^2;
                b:=max(p^2-q^2, 2*p*q);
                a:=min(p^2-q^2, 2*p*q);
                if c^2>NumberTheory:-Radical(c*b*a) then
                    l:=[op(l), [c, b, a]];
                fi
            fi
        od
    od;
    return seq((sort(l)[i])[3], i=1..nops(l));
end proc:
A366674(15641);

Crossrefs

Cf. A366428, A366675.

Sequence in context: A249333 A372934 A020691 * A145830 A195563 A250292

Adjacent sequences: A366671 A366672 A366673 * A366675 A366676 A366677

Keyword

nonn

Author

Felix Huber, Oct 16 2023

Status

approved