cp's OEIS Frontend

A298907 Primitive cyclic quadrilaterals with integer area.

%I A298907 #16 Nov 07 2018 03:53:46
%S A298907 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,
%T A298907 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,
%U A298907 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
%N A298907 Primitive cyclic quadrilaterals with integer area.
%C A298907 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.
%C A298907 It appears that the number of odd sidelengths in any quadruple is always 0, 2, or 4.
%e A298907 We list here the early quadruplets, in parentheses, augmented by the associated perimeter and area to justify the ordering of the quadruplets:
%e A298907 (a,  b,  c,  d)  Perim  Area
%e A298907 ===============  =====  ====
%e A298907 (1,  3,  6,  8)    18    12
%e A298907 (1,  5,  5,  7)    18    16
%e A298907 (1,  2,  8,  9)    20    12
%e A298907 (1,  5,  5,  9)    20    15
%e A298907 (1,  4,  7,  8)    20    18
%e A298907 (2,  5,  5,  8)    20    20
%e A298907 (2,  5,  5, 10)    22    18
%e A298907 (3,  5,  5,  9)    22    24
%e A298907 (2,  4,  7, 11)    24    20
%e A298907 (3,  5,  5, 11)    24    21
%e A298907 (4,  5,  5, 10)    24    28
%e A298907 (2,  6,  7,  9)    24    30
%e A298907 etc.
%Y A298907 Cf. A298860, A297790, A210250, A230136, A131020, A218431, A219225, A233315, A242778, A273691, A273890.
%K A298907 nonn,tabf
%O A298907 1,2
%A A298907 _Gregory Gerard Wojnar_, Jan 28 2018