cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A330909 Floor of area of triangle whose sides are consecutive Ulam numbers (A002858).

This page as a plain text file.
%I A330909 #15 Jun 20 2022 07:11:08
%S A330909 0,2,5,11,23,43,70,100,141,227,361,478,670,826,1044,1183,1405,1668,
%T A330909 1960,2272,2545,2889,3351,3819,4267,4523,4955,5669,6558,7474,8203,
%U A330909 8914,9633,10813,12245,13611,13972,14587,15473,16798,17987,19298,20229,21909,23166
%N A330909 Floor of area of triangle whose sides are consecutive Ulam numbers (A002858).
%C A330909 It has been proved that three consecutive Ulam numbers U(n) for n > 1 satisfy the triangle inequality. See Wikipedia link below.
%H A330909 Alois P. Heinz, <a href="/A330909/b330909.txt">Table of n, a(n) for n = 1..1000</a>
%H A330909 Wikipedia, <a href="http://en.wikipedia.org/wiki/Ulam_number">Ulam number</a>.
%F A330909 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 A330909 a(2) = 2 because the triangle with sides (2, 3, 4) has area 3*sqrt(15)/4 = 2.9047...
%t A330909 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 A330909 Cf. A002858, A331729.
%K A330909 nonn
%O A330909 1,2
%A A330909 _Frank M Jackson_, May 01 2020