Relationships To Other Kinds of Numbers
Geometrically, the nth star number is made up of a central point and 12 copies of the (n−1)th triangular number — making it numerically equal to the nth centered dodecagonal number, but differently arranged.
Infinitely many star numbers are also triangular numbers, the first four being S1 = 1 = T1, S7 = 253 = T22, S91 = 49141 = T313, and S1261 = 9533161 = T4366 (sequence A156712 in OEIS).
Infinitely many star numbers are also square numbers, the first four being S1 = 12, S5 = 121 = 112, S45 = 11881 = 1092, and S441 = 1164241 = 10792 (sequence A054318 in OEIS).
A star prime is a star number that is prime. The first few star primes (sequence A083577 in OEIS) are 13, 37, 73, 181, 337, 433, 541, 661, 937.
The term "star number" or "stellate number" is occasionally used to refer to octagonal numbers.
Read more about this topic: Star Number
Famous quotes containing the words kinds and/or numbers:
“Two kinds of blindness are easily combined so that those who do not see really appear to see what is not.”
—Tertullian (c. 150–230)
“The barriers of conventionality have been raised so high, and so strangely cemented by long existence, that the only hope of overthrowing them exists in the union of numbers linked together by common opinion and effort ... the united watchword of thousands would strike at the foundation of the false system and annihilate it.”
—Mme. Ellen Louise Demorest 1824–1898, U.S. women’s magazine editor and woman’s club movement pioneer. Demorest’s Illustrated Monthly and Mirror of Fashions, p. 203 (January 1870)