A057100 Hypotenuses of Pythagorean triangles (ordered by the product of the sides).

5, 10, 13, 15, 17, 20, 25, 26, 25, 29, 30, 41, 37, 34, 35, 39, 40, 50, 61, 45, 52, 51, 50, 65, 53, 55, 85, 58, 65, 60, 75, 82, 65, 74, 68, 65, 70, 78, 113, 73, 101, 75, 85, 80, 85, 91, 100, 89, 85, 122, 87, 90, 145, 123, 104, 95, 111, 102, 97, 100, 145, 130, 125, 106

Offset

1,1

Links

Table of n, a(n) for n=1..64.

Formula

a(n) =A057096(n)/(A057098(n)*A057099(n)) =sqrt(A057098(n)^2+A057099(n)^2)

Example

a(1)=5 since 3*4*5=60 is smallest possible positive product

Mathematica

maxShortLeg = 66; terms = 64;
r[a_] := {a, b, c} /. {ToRules[Reduce[a <= b < c && a^2+b^2 == c^2, {b, c}, Integers]]};
abc = r /@ Complement[Range[maxShortLeg], {1, 2, 4}] // Flatten[#, 1]&;
SortBy[abc, Times @@ # &][[;; terms, 3]] (* Jean-François Alcover, Nov 21 2019 *)

Crossrefs

Cf. A009000, A057096.

Sequence in context: A324928 A009000 A198389 * A304436 A009003 A071821

Adjacent sequences: A057097 A057098 A057099 * A057101 A057102 A057103

Keyword

nonn

Author

Henry Bottomley, Aug 01 2000

Status

approved