Centered triangular number

A centered triangular number is a number that according to the formula

Can be calculated from a natural number. The first centered triangular numbers are

The centered triangular numbers are like the centered square numbers and the centered five-and Sechseckszahlen to the centered Polygonalzahlen, ie, to the plane figurate numbers

The centered triangular numbers quantify namely, the number of stones to create a triangle using the following rule: There is a stone in the center and around this other stones are arranged in triangular layers. The number of tesserae in such an arrangement with layers is referred to as TE - centered triangular number.

For each centered triangular number can be represented as the sum of three consecutive normal triangular numbers. Furthermore, is that integer division by an arbitrary triangular number 3 always yields the residue 1 and the quotient the previous triangular number.

The sum of the first triangular numbers ( ) gives the magic constant ( row total ) a magic square of the numbers 1 to.

Centered Triangle primes

A centered triangle number, which is a prime number, is referred to as a triangle centered prime. The first centered triangle prime numbers are: