A120127 - OEIS

%I #33 Jan 07 2020 10:51:56

%S 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,

%T 54,57,59,62,64,67,71,72,76,78,79,81,83,84,86,94,98,99,103,107,108,

%U 118,121,122,124,127,128,129,131,133,134,135,139,142,151,152,155,158,162

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

%C 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

%H Ray Chandler, <a href="/A120127/b120127.txt">Table of n, a(n) for n = 1..10000</a> (first 1500 terms from Frank M Jackson)

%H Sascha Kurz, <a href="http://hdl.handle.net/10525/382">On the generation of Heronian triangles</a>, Serdica Journal of Computing. 2 (2) (2008): pp. 181-196.

%H Sascha Kurz, <a href="http://www.wm-archive.uni-bayreuth.de/index.php?id=554&amp;L=3">Lists of primitive Heronian triples</a>, Bayreuth University.

%H Michael Somos, <a href="http://grail.eecs.csuohio.edu/~somos/tritab.html">Heronian Triangle Table</a>

%H P. Yiu, <a href="http://math.fau.edu/yiu/RecreationalMathematics2003.pdf">Heron triangles with sides < 100</a>, Recreational Mathematics, Appendix Chap. 9.3 pp. 81/360. (This is a download of 360 pages.)

%t 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 *)

%K nonn

%O 1,2

%A _Lekraj Beedassy_, Jun 10 2006