A240240 Consider primitive Heronian triangles with integer area and with sides {m, m+1, c}, where c > m+1. The sequence gives the possible values of m.

3, 9, 13, 19, 20, 33, 51, 65, 73, 99, 119, 129, 163, 170, 174, 193, 201, 203, 220, 243, 260, 269, 287, 289, 339, 362, 377, 393, 450, 451, 513, 532, 559, 579, 615, 649, 696, 702, 714, 723, 740, 771, 801, 883, 909, 940, 969, 975, 1059, 1112, 1153, 1155, 1156, 1164, 1251, 1299, 1325, 1332, 1353, 1424, 1455, 1459, 1569, 1605, 1615, 1683, 1690, 1716, 1801, 1869, 1919, 1923

Offset

1,1

Comments

Corresponding values of c are 5, 17, 15, 37, 29, 65, 101, 109, 145.

And corresponding values of area/6 are 1, 6, 14, 19, 35, 44, 85, 330, 146, 231, 1190.

The sequence includes all terms of A016064 (where c = m+2) except for the first term, 1 (case with zero area).

Note that in all cases c is odd and m+2 <= c < 2m+1.

Links

Table of n, a(n) for n=1..72.

Example

First triangle has sides (3,4,5) and area 6.
2nd triangle has sides (9,10,17) and area 36.
3rd triangle has sides (13,14,15) and area 84.

Mathematica

re=Reap[Do[a=m; b=m+1; Do[s=(a+b+c)/2; area=Sqrt[s(s-a)(s-b)(s-c)]; If[IntegerQ[area], Sow[{a, b, c, area}]; Break[]], {c, 2m-1, m+2, -2 }], {m, 3, 2000}]][[2, 1]]; #[[1]]&/@ re

Crossrefs

Cf. A083875, A016064, A224301, A227003, A239978, A227166.

Sequence in context: A075326 A298870 A095234 * A032415 A268044 A190745

Adjacent sequences: A240237 A240238 A240239 * A240241 A240242 A240243

Keyword

nonn

Author

Zak Seidov, Apr 03 2014

Status

approved