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

1,2

Comments

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

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Wikipedia, Ulam number.

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.

Example

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

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

Crossrefs

Cf. A002858, A331729.

Sequence in context: A062475 A186265 A225947 * A281969 A124920 A064934

Adjacent sequences: A330906 A330907 A330908 * A330910 A330911 A330912

Keyword

nonn

Author

Frank M Jackson, May 01 2020

Status

approved