login
A057100
Hypotenuses of Pythagorean triangles (ordered by the product of the sides).
7
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
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
Sequence in context: A324928 A009000 A198389 * A304436 A009003 A071821
KEYWORD
nonn
AUTHOR
Henry Bottomley, Aug 01 2000
STATUS
approved