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A057099
Middle side of a Pythagorean triangle (ordered by the product of the sides).
5
4, 8, 12, 12, 15, 16, 24, 24, 20, 21, 24, 40, 35, 30, 28, 36, 32, 48, 60, 36, 48, 45, 40, 63, 45, 44, 84, 42, 60, 48, 72, 80, 56, 70, 60, 52, 56, 72, 112, 55, 99, 60, 77, 64, 75, 84, 96, 80, 68, 120, 63, 72, 144, 120, 96, 76, 105, 90, 72, 80, 143, 126, 120, 90, 84, 108, 91
OFFSET
1,1
FORMULA
a(n) =A057096(n)/(A057098(n)*A057100(n)) =sqrt(A057100(n)^2-A057098(n)^2)
EXAMPLE
a(1)=4 since 3*4*5=60 is smallest possible positive product
MATHEMATICA
maxShortLeg = 66; terms = 67;
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, 2]] (* Jean-François Alcover, Nov 21 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, Aug 01 2000
STATUS
approved