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

Author

Felix Huber, Jan 18 2025

Keywords

• nonn

Comments

Corresponding hypotenuses in A380072, short legs in A380074.

Subsequence of A046084 and supersequence of A089548.

Examples

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

Links

• Felix Huber, Table of n, a(n) for n = 1..10001
• Eric Weisstein's World of Mathematics, Pythagorean Triple

Crossrefs

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

Programs

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);