A263772 Perimeters of integer-sided scalene triangles.

9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79

Offset: 1

Author

Rick L. Shepherd, Oct 27 2015

Keywords

• nonn
• easy

Comments

All natural numbers larger than 8 except 10.

Equivalently, numbers n that can be partitioned into three distinct parts a, b, and c, where a + b > c, a + c > b, and b + c > a (or, without loss of generality, into (a, b, c) with a < b < c < a + b). A subsequence of A009005. The unique terms in A107576.

For k > 2, (k-1, k, k+1) gives perimeter 3k and (k-1, k+1, k+2) gives perimeter 3k + 2. For k > 3, the scalene triangle (k-1, k, k+2) has perimeter 3k + 1.

Examples

			The integer-sided scalene triangle of least perimeter has sides of lengths 2, 3, and 4, so a(1) = 2 + 3 + 4 = 9.
		

Crossrefs

Cf. A005044, A009005, A107572, A107576.

Programs

PARI

vector(100, n, if(n==1, 9, n+9)) \\ Altug Alkan, Oct 28 2015

Formula

a(n) = n + 9 for n > 1.