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A057098
Shortest side of a Pythagorean triangle (ordered by the product of the sides).
5
3, 6, 5, 9, 8, 12, 7, 10, 15, 20, 18, 9, 12, 16, 21, 15, 24, 14, 11, 27, 20, 24, 30, 16, 28, 33, 13, 40, 25, 36, 21, 18, 33, 24, 32, 39, 42, 30, 15, 48, 20, 45, 36, 48, 40, 35, 28, 39, 51, 22, 60, 54, 17, 27, 40, 57, 36, 48, 65, 60, 24, 32, 35, 56, 63, 45, 60, 19, 66, 44, 56
OFFSET
1,1
FORMULA
a(n) =A057096(n)/(A057099(n)*A057100(n)) =sqrt(A057100(n)^2-A057099(n)^2)
EXAMPLE
a(1)=3 since 3*4*5=60 is smallest possible positive product
MATHEMATICA
maxShortLeg = 66; terms = 71;
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, 1]] (* Jean-François Alcover, Nov 21 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, Aug 01 2000
STATUS
approved