A316846 -id:A316846 - cp's OEIS frontend

A316842 Three-column table read by rows giving primitive integer sides of proper triangles (i,j,k) with i >= j >= k >= 1, j+k > i, gcd(i,j,k) = 1.

1, 1, 1, 2, 2, 1, 3, 2, 2, 3, 3, 1, 3, 3, 2, 4, 3, 2, 4, 3, 3, 4, 4, 1, 4, 4, 3, 5, 3, 3, 5, 4, 2, 5, 4, 3, 5, 4, 4, 5, 5, 1, 5, 5, 2, 5, 5, 3, 5, 5, 4, 6, 4, 3, 6, 5, 2, 6, 5, 3, 6, 5, 4, 6, 5, 5, 6, 6, 1, 6, 6, 5, 7, 4, 4, 7, 5, 3, 7, 5, 4, 7, 5, 5, 7, 6, 2, 7, 6, 3, 7, 6, 4, 7, 6, 5, 7, 6, 6, 7, 7, 1, 7, 7, 2, 7, 7, 3, 7, 7, 4, 7, 7, 5, 7, 7, 6, 8, 5, 4

Offset: 1

N. J. A. Sloane, Jul 23 2018, following a suggestion from Donald S. McDonald

			Table begins:
[1,1,1],
[2,2,1],
[3,2,2],
[3,3,1],
[3,3,2],
[4,3,2],
[4,3,3],
[4,4,1],
[4,4,3],
[5,3,3],
[5,4,2],
...

Lars Blomberg, Table of n, a(n) for n = 1..9000

There are A123323(k) rows that begin with k.
The three columns are A316846, A316847, A316848.
A316850 is a compressed version.
See A316841 for all triples (including imprimitive triples).
See A316852 and A317181 & A317183 for perimeter and area.
Other related sequences: A051493, A070080, A070081, A070082, A070110.

A316847 Column 2 of table A316842.

Original entry on oeis.org

1, 2, 2, 3, 3, 3, 3, 4, 4, 3, 4, 4, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 6, 6, 4, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 5, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 9

Offset: 1

N. J. A. Sloane, Jul 23 2018

nonn

Lars Blomberg, Table of n, a(n) for n = 1..3000

Cf. A316842, A316846, A316848.

Terms a(54) and beyond from Lars Blomberg, Jul 27 2018

A316848 Column 3 of table A316842.

Original entry on oeis.org

1, 1, 2, 1, 2, 2, 3, 1, 3, 3, 2, 3, 4, 1, 2, 3, 4, 3, 2, 3, 4, 5, 1, 5, 4, 3, 4, 5, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 4, 5, 3, 5, 2, 3, 4, 5, 6, 7, 1, 3, 5, 7, 5, 4, 5, 3, 4, 5, 6, 7, 2, 3, 4, 5, 6, 7, 8, 1, 2, 4, 5, 7, 8, 5, 4, 5, 6, 7, 3, 5, 7, 2, 3, 4, 5, 6

Offset: 1

N. J. A. Sloane, Jul 23 2018

nonn

Lars Blomberg, Table of n, a(n) for n = 1..3000

Cf. A316842, A316846, A316847.

Terms a(54) and beyond from Lars Blomberg, Jul 27 2018

A316852 Consider primitive integer triangles as listed in rows of table A316842. Sequence gives perimeters of these triangles in the same order.

Original entry on oeis.org

3, 5, 7, 7, 8, 9, 10, 9, 11, 11, 11, 12, 13, 11, 12, 13, 14, 13, 13, 14, 15, 16, 13, 17, 15, 15, 16, 17, 15, 16, 17, 18, 19, 15, 16, 17, 18, 19, 20, 17, 18, 17, 19, 17, 18, 19, 20, 21, 22, 17, 19, 21, 23, 19, 19, 20, 19, 20, 21, 22, 23, 19, 20, 21, 22, 23, 24

Offset: 1

N. J. A. Sloane, Jul 23 2018

nonn

The only missing numbers are 1,2,4,6.

Lars Blomberg, Table of n, a(n) for n = 1..3000

Cf. A316841, A316842, A316851.

a(n) = A316846(n)+A316847(n)+A316848(n).

Terms a(54) and beyond from Lars Blomberg, Jul 27 2018

A317181 Consider primitive integer triangles as listed in rows of table A316842. Sequence gives 16*area^2 for these triangles in the same order.

Original entry on oeis.org

3, 15, 63, 35, 128, 135, 320, 63, 495, 275, 231, 576, 975, 99, 384, 819, 1344, 455, 351, 896, 1575, 2304, 143, 2975, 735, 675, 1536, 2499, 495, 1280, 2295, 3456, 4655, 195, 768, 1683, 2880, 4275, 5760, 1071, 2304, 935, 3591, 663, 1728, 3135, 4800, 6615, 8448, 255, 2223, 5775, 10143

Offset: 1

N. J. A. Sloane, Jul 23 2018

Lars Blomberg, Table of n, a(n) for n = 1..3000

Cf. A316842, A316852, A316846, A316847, A316848.

Subsequence of A316853.

a(n) = 16*s*(s-a)*(s-b)*(s-c) where s = A316852(n)/2, and a,b,c are A316843(n), A316844(n), A316845(n).

cp's OEIS Frontend

A316842 Three-column table read by rows giving primitive integer sides of proper triangles (i,j,k) with i >= j >= k >= 1, j+k > i, gcd(i,j,k) = 1.

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A316847 Column 2 of table A316842.

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A316848 Column 3 of table A316842.

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A316852 Consider primitive integer triangles as listed in rows of table A316842. Sequence gives perimeters of these triangles in the same order.

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A317181 Consider primitive integer triangles as listed in rows of table A316842. Sequence gives 16*area^2 for these triangles in the same order.

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