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A350347 Consider primitive 120-degree integer triangles with sides A < B < C = A002476(n). This sequence gives the values of B. 2
5, 8, 16, 24, 33, 35, 56, 45, 63, 51, 57, 77, 95, 120, 91, 115, 143, 112, 105, 175, 165, 195, 168, 145, 224, 261, 217, 192, 288, 247, 320, 272, 280, 315, 273, 259, 385, 304, 399, 407, 299, 287, 440, 437, 301, 387, 425, 533, 416, 368, 575, 520, 423, 459, 616, 517, 441, 400, 539, 616, 637, 600, 480, 520, 728, 735, 725 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Wikipedia, Integer triangle
FORMULA
Let A = A349772(n). A^2 + A*B + B^2 = C^2.
EXAMPLE
n | ( A, B, C)
----+-------------
1 | ( 3, 5, 7)
2 | ( 7, 8, 13)
3 | ( 5, 16, 19)
4 | (11, 24, 31)
5 | ( 7, 33, 37)
6 | (13, 35, 43)
7 | ( 9, 56, 61)
8 | (32, 45, 67)
9 | (17, 63, 73)
PROG
(Ruby)
require 'prime'
def A(n)
(1..n).each{|a|
(a + 1..n).each{|b|
return b if a * a + a * b + b * b == n * n
}
}
end
def A350347(n)
ary = []
i = 1
while ary.size < n
ary << A(i) if i.prime? && i % 6 == 1
i += 1
end
ary
end
p A350347(100)
CROSSREFS
Sequence in context: A229849 A357276 A088586 * A073136 A063924 A340997
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 26 2021
STATUS
approved

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Last modified April 18 04:31 EDT 2024. Contains 371767 sequences. (Running on oeis4.)