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

1,1

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.

Links

Table of n, a(n) for n=1..70.

Formula

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

Example

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

Prog

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

Crossrefs

Cf. A005044, A009005, A107572, A107576.

Sequence in context: A098728 A233408 A107576 * A031954 A043631 A043698

Adjacent sequences: A263769 A263770 A263771 * A263773 A263774 A263775

Keyword

nonn,easy

Author

Rick L. Shepherd, Oct 27 2015

Status

approved