A087484 Least hypotenuse of a primitive Pythagorean triangle with inradius n.

5, 13, 17, 41, 37, 29, 65, 145, 101, 53, 145, 65, 197, 85, 73, 545, 325, 125, 401, 97, 109, 173, 577, 185, 677, 229, 785, 137, 901, 157, 1025, 2113, 205, 365, 169, 185, 1445, 445, 265, 233, 1765, 205, 1937, 241, 221, 629, 2305, 617, 2501, 733, 409, 305, 2917, 845

Offset

1,1

Comments

Least hypotenuse which is 2n short of the sum of the legs of a primitive Pythagorean triangle.

Links

Robert Israel, Table of n, a(n) for n = 1..10000 (correcting b-file from Ray Chandler)

Maple

f:= proc(r) local F, x, y, ys, ps, a, b, c;
     F:= ifactors(r)[2];
     ys:= map(proc(s) local t;  mul(t[1]^t[2], t=s) end proc, combinat:-powerset(F));
     if r::even then ys:= select(y -> (r/y)::odd, ys) fi;
     ps:= map(y -> 4*y^2 + 6*r + 2*r^2/y^2, ys);
     y:= ys[min[index](ps)];
     x:= y + r/y;
     x^2+y^2;
end proc:
map(f, [$1..60]); # Robert Israel, Jan 26 2026

Crossrefs

Cf. A020887, A099776 (largest hypotenuse).

Sequence in context: A188131 A172459 A120130 * A019382 A330732 A276260

Adjacent sequences: A087481 A087482 A087483 * A087485 A087486 A087487

Keyword

nonn

Author

Lekraj Beedassy, Oct 23 2003

Extensions

More terms from Ray Chandler, Oct 25 2003

Name simplified by Ray Chandler, Jan 26 2020

Deleted a link to a bad web site - N. J. A. Sloane, Jan 26 2020

Status

approved