A298907 Primitive cyclic quadrilaterals with integer area.

1, 3, 6, 8, 1, 5, 5, 7, 1, 2, 8, 9, 1, 5, 5, 9, 1, 4, 7, 8, 2, 5, 5, 8, 2, 5, 5, 10, 3, 5, 5, 9, 2, 4, 7, 11, 3, 5, 5, 11, 4, 5, 5, 10, 2, 6, 7, 9, 4, 5, 5, 12, 3, 4, 8, 11, 4, 5, 7, 10, 2, 5, 10, 11, 1, 7, 8, 14, 1, 8, 9, 12, 3, 7, 9, 11, 1, 6, 10, 15, 2, 7, 9, 14, 1, 7, 11, 13, 6, 7, 8, 11, 1, 10, 10, 13, 2, 9, 11, 12, 3, 6, 13, 14, 3, 8, 10, 15

Offset

1,2

Comments

Entries are listed as quadruples: (a,b,c,d). They are ordered first by perimeter, second by area, then by a, then b, then c, then d. Rectangles and kites with two right angles are not listed; thus a < b <= c <= d. By "primitive" we mean (a,b,c,d) is not a multiple of any earlier quadruple.

It appears that the number of odd sidelengths in any quadruple is always 0, 2, or 4.

Links

Table of n, a(n) for n=1..108.

Example

We list here the early quadruplets, in parentheses, augmented by the associated perimeter and area to justify the ordering of the quadruplets:
(a,  b,  c,  d)  Perim  Area
===============  =====  ====
(1,  3,  6,  8)    18    12
(1,  5,  5,  7)    18    16
(1,  2,  8,  9)    20    12
(1,  5,  5,  9)    20    15
(1,  4,  7,  8)    20    18
(2,  5,  5,  8)    20    20
(2,  5,  5, 10)    22    18
(3,  5,  5,  9)    22    24
(2,  4,  7, 11)    24    20
(3,  5,  5, 11)    24    21
(4,  5,  5, 10)    24    28
(2,  6,  7,  9)    24    30
etc.

Crossrefs

Cf. A298860, A297790, A210250, A230136, A131020, A218431, A219225, A233315, A242778, A273691, A273890.

Sequence in context: A133442 A133193 A200131 * A181909 A181917 A157032

Adjacent sequences: A298904 A298905 A298906 * A298908 A298909 A298910

Keyword

nonn,tabf

Author

Gregory Gerard Wojnar, Jan 28 2018

Status

approved