Star Number

A star number is a centered figurate number whose dots form a six-pointed star, or hexagram, the same shape as the Star of David or a Chinese checkers board. The nth star number is given by the formula six times n times n minus one, plus one, and the sequence runs one, thirteen, thirty-seven, seventy-three, one hundred twenty-one, one hundred eighty-one and on without end. Because the same points can also be read as a twelve-sided centered polygon, star numbers are also called centered dodecagonal numbers, and each one is built from a central point plus twelve copies of the previous triangular number. The number thirty-five thousand one hundred thirteen is unusual because its own prime factors, thirteen, thirty-seven and seventy-three, are themselves three consecutive star numbers.