Star number
A centered figurate number forming a six-pointed star.
A star number is a centered figurate number that forms a six-pointed star, like the Star of David. It is also known as a centered dodecagonal number because it can be arranged as a twelve-sided polygon. The nth star number is given by the formula Sn = 6n(n − 1) + 1.
Quick Facts
- Number
- infinity
- First terms
- 1, 13, 37, 73, 121, 181
Facts from the source article.
Relationships to other kinds of numbers
Geometrically, the nth star number consists of a central point plus 12 copies of the (n−1)th triangular number, making it numerically equal to the nth centered dodecagonal number. It can be expressed as Sn = 1 + 12Tn−1, where Tn = n(n+1)/2. Infinitely many star numbers are also triangular numbers; the first four are S1 = 1 = T1, S7 = 253 = T22, S91 = 49141 = T313, and S1261 = 9533161 = T4366. A star prime is a star number that is prime; the first few are 13, 37, 73, 181, 337, 433, 541, 661, 937. A superstar prime is a star prime whose prime index is also a star number; the first two are 661 and 1750255921. A reverse superstar prime is a star number whose index is a star prime; the first few are 937, 7993, 31537, 195481, 679393, 1122337, 1752841, 2617561, 5262193. The term "star number" or "stellate number" is occasionally used for octagonal numbers.
More in Star of David
Spotted an error? Know more?
Reader corrections go straight into our review queue. Suggest an edit · How this site is sourced