A107576 -id:A107576 - cp's OEIS frontend

A107572 List of triples a,b,c that are sidelengths of a scalene triangle; a

2, 3, 4, 2, 4, 5, 3, 4, 5, 2, 5, 6, 3, 4, 6, 3, 5, 6, 2, 6, 7, 3, 5, 7, 4, 5, 6, 3, 6, 7, 4, 5, 7, 2, 7, 8, 3, 6, 8, 4, 5, 8, 4, 6, 7, 3, 7, 8, 4, 6, 8, 5, 6, 7, 2, 8, 9, 3, 7, 9, 4, 6, 9, 4, 7, 8, 5, 6, 8, 3, 8, 9, 4, 7, 9, 5, 6, 9, 5, 7, 8, 2, 9, 10, 3, 8, 10, 4, 7, 10, 4, 8, 9, 5, 6, 10, 5, 7, 9, 6, 7, 8, 3

Offset: 1

Clark Kimberling, May 16 2005

The number of such triangles of perimeter n+6 is Alcuin's sequence, as noted at A005044.

			(2,3,4) is the least such triangle, followed by (2,4,5) and then (3,4,5).

Cf. A107573, A107574, A107575, A107576, A107577, A005044, A070080.

A107573 a(n)=least sidelength of n-th triangle listed at A107572.

Original entry on oeis.org

2, 2, 3, 2, 3, 3, 2, 3, 4, 3, 4, 2, 3, 4, 4, 3, 4, 5, 2, 3, 4, 4, 5, 3, 4, 5, 5, 2, 3, 4, 4, 5, 5, 6, 3, 4, 5, 5, 6, 2, 3, 4, 4, 5, 5, 6, 6, 3, 4, 5, 5, 6, 6, 7, 2, 3, 4, 4, 5, 5, 6, 6, 6, 7, 3, 4, 5, 5, 6, 6, 7, 7, 2, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 3, 4, 5, 5, 6, 6, 7, 7, 7, 8, 2, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7

Offset: 1

Clark Kimberling, May 16 2005

nonn

			The first 5 integer-sided scalene triangles (a,b,c) with a<b<c are (2,3,4), (2,4,5), (3,4,5), (2,5,6), (3,4,6), of which the least sidelengths are 2,2,3,2,3

Cf. A107572, A107574, A107575, A107576, A107577, A005044, A070080.

A107574 a(n)=middle sidelength of n-th triangle listed at A107572.

Original entry on oeis.org

3, 4, 4, 5, 4, 5, 6, 5, 5, 6, 5, 7, 6, 5, 6, 7, 6, 6, 8, 7, 6, 7, 6, 8, 7, 6, 7, 9, 8, 7, 8, 6, 7, 7, 9, 8, 7, 8, 7, 10, 9, 8, 9, 7, 8, 7, 8, 10, 9, 8, 9, 7, 8, 8, 11, 10, 9, 10, 8, 9, 7, 8, 9, 8, 11, 10, 9, 10, 8, 9, 8, 9, 12, 11, 10, 11, 9, 10, 8, 9, 10, 8, 9, 9, 12, 11, 10, 11, 9, 10, 8, 9, 10, 9, 13

Offset: 1

Clark Kimberling, May 16 2005

nonn

			The first 5 integer-sided scalene triangles (a,b,c) with a<b<c are (2,3,4), (2,4,5), (3,4,5), (2,5,6), (3,4,6), of which the middle sidelengths are 3,4,4,5,4.

Cf. A107572, A107573, A107575, A107576, A107577, A005044, A070080.

A107575 a(n)=greatest sidelength of n-th triangle listed at A107572.

Original entry on oeis.org

4, 5, 5, 6, 6, 6, 7, 7, 6, 7, 7, 8, 8, 8, 7, 8, 8, 7, 9, 9, 9, 8, 8, 9, 9, 9, 8, 10, 10, 10, 9, 10, 9, 8, 10, 10, 10, 9, 9, 11, 11, 11, 10, 11, 10, 10, 9, 11, 11, 11, 10, 11, 10, 9, 12, 12, 12, 11, 12, 11, 12, 11, 10, 10, 12, 12, 12, 11, 12, 11, 11, 10, 13, 13, 13, 12, 13, 12, 13, 12, 11

Offset: 1

Clark Kimberling, May 16 2005

nonn

			The first 5 integer-sided scalene triangles (a,b,c) with a<b<c are (2,3,4), (2,4,5), (3,4,5), (2,5,6), (3,4,6), of which the greatest sidelengths are 4,5,5,6,6.

Cf. A107572, A107573, A107574, A107576, A107577, A005044, A070080.

A263772 Perimeters of integer-sided scalene triangles.

Original entry on oeis.org

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

Rick L. Shepherd, Oct 27 2015

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.

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

Cf. A005044, A009005, A107572, A107576.

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

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

cp's OEIS Frontend

A107572 List of triples a,b,c that are sidelengths of a scalene triangle; a

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A107573 a(n)=least sidelength of n-th triangle listed at A107572.

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A107574 a(n)=middle sidelength of n-th triangle listed at A107572.

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A107575 a(n)=greatest sidelength of n-th triangle listed at A107572.

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A263772 Perimeters of integer-sided scalene triangles.

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