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A298907 Primitive cyclic quadrilaterals with integer area. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 23 09:35 EDT 2019. Contains 322385 sequences. (Running on oeis4.)