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 A335035 Ordered perimeters of primitive integer triangles with two perpendicular medians. 6
 54, 70, 104, 154, 170, 216, 252, 266, 352, 368, 418, 442, 464, 594, 598, 620, 638, 720, 740, 748, 792, 810, 902, 952, 962, 988, 1054, 1102, 1118, 1134, 1148, 1170, 1216, 1274, 1316, 1376, 1426, 1484, 1512, 1564, 1568, 1598, 1600, 1638, 1702, 1710, 1802, 1836, 1862 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The study of these integer triangles that have two perpendicular medians was proposed in the problem of Concours Général in 2007 in France (see link). If medians issued of A and B are perpendicular in centroid G, then a^2 + b^2 = 5 * c^2 (see Maths Challenge picture in link). All terms are even because each triple is composed of one even side and two odd sides. For the corresponding primitive triples and miscellaneous properties, see A335034. LINKS Annales Concours Général, Sujet Concours Général 2007 Maths Challenge, Perpendicular medians, Problem with picture. FORMULA a(n) = A335036(n) + A335037(n) + A335038(n). EXAMPLE a(1) = 13 + 19 + 22 = 54 with 19^2 + 22^2 = 5 * 13^2 = 845. PROG (PARI) lista(nn) = {my(vm = List(), vt); for (u=1, nn, for (v=1, nn, if (gcd(u, v) == 1, vt = 0; if ((u/v > 3) && ((u-3*v) % 5), vt = [2*(u^2-u*v-v^2), u^2+4*u*v-v^2, u^2+v^2]); if ((u/v > 1) && (u/v < 2) && ((u-2*v) % 5), vt = [2*(u^2+u*v-v^2), -u^2+4*u*v+v^2, u^2+v^2]); if ((gcd(vt) == 1), listput(vm, vecsum(vt))); ); ); ); vecsort(vm); } \\ Michel Marcus, May 27 2020 CROSSREFS Cf. A024364 (perimeters of primitive Pythagorean triangles). Cf. A335034 (corresponding primitive triples), A335036 (smallest side), A335037 (middle side), A335038 (largest side), A335273 (even side). Sequence in context: A025331 A025323 A157934 * A281920 A005129 A039532 Adjacent sequences:  A335032 A335033 A335034 * A335036 A335037 A335038 KEYWORD nonn AUTHOR Bernard Schott, May 27 2020 STATUS approved

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Last modified September 18 03:39 EDT 2020. Contains 337164 sequences. (Running on oeis4.)