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

0, 2, 5, 11, 23, 43, 70, 100, 141, 227, 361, 478, 670, 826, 1044, 1183, 1405, 1668, 1960, 2272, 2545, 2889, 3351, 3819, 4267, 4523, 4955, 5669, 6558, 7474, 8203, 8914, 9633, 10813, 12245, 13611, 13972, 14587, 15473, 16798, 17987, 19298, 20229, 21909, 23166

Offset: 1

Author

Frank M Jackson, May 01 2020

Keywords

• nonn

Comments

It has been proved that three consecutive Ulam numbers U(n) for n > 1 satisfy the triangle inequality. See Wikipedia link below.

Examples

			a(2) = 2 because the triangle with sides (2, 3, 4) has area 3*sqrt(15)/4 = 2.9047...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000
• Wikipedia, Ulam number.

Crossrefs

Cf. A002858, A331729.

Programs

Mathematica

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

Formula

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.