|
%I #15 Jun 20 2022 07:11:08
%S 0,2,5,11,23,43,70,100,141,227,361,478,670,826,1044,1183,1405,1668,
%T 1960,2272,2545,2889,3351,3819,4267,4523,4955,5669,6558,7474,8203,
%U 8914,9633,10813,12245,13611,13972,14587,15473,16798,17987,19298,20229,21909,23166
%N Floor of area of triangle whose sides are consecutive Ulam numbers (A002858).
%C It has been proved that three consecutive Ulam numbers U(n) for n > 1 satisfy the triangle inequality. See Wikipedia link below.
%H Alois P. Heinz, <a href="/A330909/b330909.txt">Table of n, a(n) for n = 1..1000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Ulam_number">Ulam number</a>.
%F Given a triangle with sides a, b and c, the area A = sqrt(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2.
%e a(2) = 2 because the triangle with sides (2, 3, 4) has area 3*sqrt(15)/4 = 2.9047...
%t lst1 = ReadList["https://oeis.org/A002858/b002858.txt", {Number,Number}]; lst={}; Do[{a, b, c}={lst1[[n]][[2]], lst1[[n+1]][[2]], lst1[[n+2]][[2]]}; s = (a+b+c)/2; A=Sqrt[s(s-a)(s-b)(s-c)]; AppendTo[lst, Floor@A], {n, 1, 50}]; lst
%Y Cf. A002858, A331729.
%K nonn
%O 1,2
%A _Frank M Jackson_, May 01 2020
|
