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A350047
Perimeters of more than one primitive 120-degree integer triangle.
3
2730, 4080, 7590, 9044, 11704, 12180, 13020, 13485, 13920, 14880, 15810, 16100, 18870, 21090, 22755, 23370, 24752, 25172, 26445, 27060, 28380, 29670, 30315, 31020, 32430, 32890, 33810, 34545, 34580, 36660, 37950, 38038, 38220, 38955, 41340, 42476, 44520, 46046, 46110
OFFSET
1,1
LINKS
EXAMPLE
897^2 + 560^2 + 897*560 = 1273^2, 168^2 + 1235^2 + 168*1235 = 1327^2 and 897 + 560 + 1273 = 168 + 1235 + 1327 = 2730. So 2730 is a term.
38640^2 + 5291^2 + 38640*5291 = 41539^2, 23088^2 + 22715^2 + 23088*22715 = 39667^2, 10857^2 + 34040^2 + 10857*34040 = 40573^2 and 38640 + 5291 + 41539 = 23088 + 22715 + 39667 = 10857 + 34040 + 40573 = 85470. So 85470 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
ary << 2 * j * j + 3 * i * j + i * i
end
}
}
ary
end
p A(200).group_by(&:to_i).select{|k, v| v.size > 1}.keys.sort[0..50]
CROSSREFS
Sequence in context: A231289 A212725 A031608 * A043579 A166780 A068305
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 11 2021
STATUS
approved