A120127 Numbers that are never the longest side of a primitive Heronian triangle.

1, 2, 3, 4, 7, 9, 10, 11, 12, 14, 16, 18, 19, 22, 23, 27, 31, 32, 33, 34, 38, 43, 46, 47, 49, 54, 57, 59, 62, 64, 67, 71, 72, 76, 78, 79, 81, 83, 84, 86, 94, 98, 99, 103, 107, 108, 118, 121, 122, 124, 127, 128, 129, 131, 133, 134, 135, 139, 142, 151, 152, 155, 158, 162

Offset

1,2

Comments

The Mathematica program below accesses a table of primitive Heronian triples (PHT) generated by Sascha Kurz (see Link). The list contains a triple for every possible PHT with a maximum side length of 10000. The triples are in the form (a,b,c) where a >= b >= c and where a <= 10000. - Frank M Jackson, Dec 04 2017

Links

Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1500 terms from Frank M Jackson)

Sascha Kurz, On the generation of Heronian triangles, Serdica Journal of Computing. 2 (2) (2008): pp. 181-196.

Sascha Kurz, Lists of primitive Heronian triples, Bayreuth University.

Michael Somos, Heronian Triangle Table

P. Yiu, Heron triangles with sides < 100, Recreational Mathematics, Appendix Chap. 9.3 pp. 81/360. (This is a download of 360 pages.)

Mathematica

lst1 = ReadList["C:/primitive_heronian_triangles_1_10000.txt", {Number, Number, Number}]; lst = Union@Table[lst1[[n]][[1]], {n, 1, Length[lst1]}]; Select[Range[10000], ! MemberQ[lst, #] &] (* For download of file of primitive Heronian triples see Link *) (* Frank M Jackson, Dec 04 2017 *)

Crossrefs

Sequence in context: A285500 A119345 A086391 * A047548 A095378 A141489

Adjacent sequences: A120124 A120125 A120126 * A120128 A120129 A120130

Keyword

nonn

Author

Lekraj Beedassy, Jun 10 2006

Status

approved