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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 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.)