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%I #20 Dec 27 2021 08:23:44
%S 5,8,16,24,33,35,56,45,63,51,57,77,95,120,91,115,143,112,105,175,165,
%T 195,168,145,224,261,217,192,288,247,320,272,280,315,273,259,385,304,
%U 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
%N Consider primitive 120-degree integer triangles with sides A < B < C = A002476(n). This sequence gives the values of B.
%H Seiichi Manyama, <a href="/A350347/b350347.txt">Table of n, a(n) for n = 1..1000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer triangle</a>
%F Let A = A349772(n). A^2 + A*B + B^2 = C^2.
%e n | ( A, B, C)
%e ----+-------------
%e 1 | ( 3, 5, 7)
%e 2 | ( 7, 8, 13)
%e 3 | ( 5, 16, 19)
%e 4 | (11, 24, 31)
%e 5 | ( 7, 33, 37)
%e 6 | (13, 35, 43)
%e 7 | ( 9, 56, 61)
%e 8 | (32, 45, 67)
%e 9 | (17, 63, 73)
%o (Ruby)
%o require 'prime'
%o def A(n)
%o (1..n).each{|a|
%o (a + 1..n).each{|b|
%o return b if a * a + a * b + b * b == n * n
%o }
%o }
%o end
%o def A350347(n)
%o ary = []
%o i = 1
%o while ary.size < n
%o ary << A(i) if i.prime? && i % 6 == 1
%o i += 1
%o end
%o ary
%o end
%o p A350347(100)
%Y Cf. A002365, A002476 (C), A229849, A264827, A349772 (A).
%K nonn
%O 1,1
%A _Seiichi Manyama_, Dec 26 2021
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