A380074 Short legs of Pythagorean triangles having legs that add up to a square ordered by increasing hypotenuse.

21, 9, 84, 36, 133, 85, 189, 81, 189, 184, 336, 144, 400, 217, 532, 525, 340, 225, 820, 756, 324, 756, 736, 1036, 57, 1029, 564, 820, 1197, 672, 765, 441, 1344, 576, 1600, 1701, 868, 2128, 729, 2100, 1701, 1656, 1360, 1464, 2044, 900, 1513, 2541, 781, 2340, 3280

Offset: 1

Author

Felix Huber, Jan 18 2025

Keywords

• nonn

Comments

Corresponding hypotenuses in A380072, long legs in A380073.

Subsequence of A046083 and supersequence of A089547.

Examples

			21 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, A046083, A089547, A379830, A380072, A380073.

Programs

Maple

# Calculates the first 10001 terms
A380074:=proc(M)
    local i,m,p,q,r,u,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
                    u:=r*min(p^2-q^2,2*p*q);
                    L:=[op(L),seq([i^2*w,i^2*u],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;
A380074(4330);