A350347 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

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