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A350039
Perimeters of more than one primitive 60-degree integer triangle.
3
1260, 2520, 2574, 3080, 3740, 3780, 3978, 4620, 4940, 5148, 5720, 5814, 5940, 6435, 6930, 7020, 7280, 7560, 7820, 7866, 7956, 8190, 8550, 8580, 8892, 9044, 10010, 10350, 10395, 10472, 10640, 11628, 11880, 12006, 12240, 12870, 12920, 13050, 13260, 13340, 13680, 13685, 13832, 13860, 13950
OFFSET
1,1
LINKS
EXAMPLE
399^2 + 440^2 - 399*440 = 421^2, 56^2 + 615^2 - 56*615 = 589^2 and 399 + 440 + 421 = 56 + 615 + 589 = 1260. So 1260 is a term.
5159^2 + 5904^2 - 5159*5904 = 5569^2, 3344^2 + 7119^2 - 3344*7119 = 6169^2, 1287^2 + 7952^2 - 1287*7952 = 7393^2 and 5159 + 5904 + 5569 = 3344 + 7119 + 6169 = 1287 + 7952 + 7393 = 16632. So 16632 is a term.
PROG
(Ruby)
def A(n)
ary = []
(1..n).each{|i|
(i + 1..n).each{|j|
if i.gcd(j) == 1 && (i - j) % 3 > 0
x, y, z = j * j, i * j, i * i
ary << 2 * x + 5 * y + 2 * z
ary << 3 * x + 3 * y
end
}
}
ary
end
p A(100).group_by(&:to_i).select{|k, v| v.size > 1}.keys.sort[0..50]
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 10 2021
STATUS
approved