Centered hexagonal number  A centered hexagonal number, or hex number, is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice. Centered hexagonal numbers have practical applications in materials logistics management. A centered hexagonal number is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice. The th centered hexagonal number is given by the formula  Expressing the formula as  shows that the centered hexagonal number for is 1 more than 6 times the th triangular number. The first few centered hexagonal numbers are :  In base 10 one can notice that the hexagonal numbers' rightmost (least significant) digits follow the pattern 1–7–9–7–1. The sum of the first centered hexagonal numbers is . That is, centered hexagonal pyramidal numbers and cubes are the same numbers, but they represent different shapes. Viewed from the opposite perspective, centered hexagonal numbers are differences of two consecutive cubes, so that the centered hexagonal numbers are the gnomon of the cubes. (This can be seen geometrically from the diagram.) In particular, prime centered hexagonal numbers are cuban primes. The difference between and the th centered hexagonal number is a number of the form , while the difference between and the th centered hexagonal number is a pronic number. Centered hexagonal numbers have practical applications in materials logistics management, for example, in packing round items into larger round containers, such as Vienna sausages into round cans, or combining individual wire strands into a cable. The root of a centered hexagonal number can be calculated using the following formula: