A380073 Long legs of Pythagorean triangles having legs that add up to a square ordered by increasing hypotenuse.

28, 40, 112, 160, 156, 204, 252, 360, 340, 345, 448, 640, 561, 744, 624, 700, 816, 1000, 861, 1008, 1440, 1360, 1380, 1173, 1624, 1372, 1645, 1581, 1404, 1729, 1836, 1960, 1792, 2560, 2244, 2268, 2976, 2496, 3240, 2800, 3060, 3105, 3264, 3577, 3285, 4000, 3816

Offset

1,1

Comments

Corresponding hypotenuses in A380072, short legs in A380074.

Subsequence of A046084 and supersequence of A089548.

Links

Felix Huber, Table of n, a(n) for n = 1..10001

Eric Weisstein's World of Mathematics, Pythagorean Triple

Example

28 is in the sequence because 21^2 + 28^2 = 35^2 and 21 + 28 = 7^2.

Maple

# Calculates the first 10001 terms
A380073:=proc(M)
    local i, m, p, q, r, v, w, L, F;
    L:=[];
    m:=M^2+2*M+2;
    for p from 2 to M do
        for q to p-1 do
            if gcd(p, q)=1 and (is(p, even) or is(q, even)) then
                r:=1;
                for i in ifactors(p^2-q^2+2*p*q)[2] do
                    if is(i[2], odd) then
                        r:=r*i[1]
                    fi
                od;
                w:=r*(p^2+q^2);
                if w<=m then
                    v:=r*max(p^2-q^2, 2*p*q);
                    L:=[op(L), seq([i^2*w, i^2*v], i=1..floor(sqrt(m/w)))]
                fi
            fi
        od
    od;
    F:=[];
    for i in sort(L) do
        F:=[op(F), i[2]]
    od;
    return op(F)
end proc;
A380073(4330);

Crossrefs

Cf. A000290, A007913, A046084, A089548, A379830, A380072, A380074.

Sequence in context: A367975 A184032 A361855 * A047630 A135789 A219882

Adjacent sequences: A380070 A380071 A380072 * A380074 A380075 A380076

Keyword

nonn,new

Author

Felix Huber, Jan 18 2025

Status

approved