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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 Seiichi Manyama, Table of n, a(n) for n = 1..1000 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 Cf. A002365, A002476 (C), A229849, A264827, A349772 (A). Sequence in context: A229849 A357276 A088586 * A073136 A063924 A340997 Adjacent sequences: A350344 A350345 A350346 * A350348 A350349 A350350 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.)