Star number - Citizendia

A star number is a centered figurate number that represents a centered hexagram, such as the one that Chinese checkers is played on. The centered polygonal numbers are a class of series of Figurate numbers each formed by a central dot surrounded by polygonal layers with a constant number of sides A figurate number is a number that can be represented as a regular and discrete geometric pattern (e For symbols used in the I Ching, see Hexagram (I Ching For a Jewish symbol see Star of David. Chinese Checkers is a Board game that can be played by two to six people The nth star number is given by the formula 6n(n - 1) + 1. The first few star numbers are

1, 13, 37, 73, 121, 181, 253, 337, 433, 541, 661, 793, 937, 1093, 1261, 1441, 1633, 1837, 2053, 2281, 2521, 2773, 3037, 3313, 3601, 3901, 4213, 4537, 4873, 5221, 5581, 5953, 6337, 6733, 7141, 7561, 7993, 8437, 8893, 9361, 9841, 10333, 10837 (sequence A003154 in OEIS). Mathematics For any number x: x ·1 = 1· x = x (1 is the multiplicative identity 37 ( thirty-seven) is the Natural number following 36 and preceding 38. 73 ( seventy-three) is the Natural number following 72 and preceding 74. 181 is the natural number between 180 and 182. In mathematics 181 is a Prime number, and a Twin prime with 179 The On-Line Encyclopedia of Integer Sequences ( OEIS) also cited simply as Sloane's, is an extensive searchable Database of Integer sequences

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 centred dodecagonal number, but differently arranged. A triangular number is the sum of the n Natural numbers from 1 to n. Regular dodecagon It usually refers to a regular dodecagon having all sides of equal length and all angles equal to 150°

The digital root of a star number is always 1 or 4. The digital root (also repeated digital sum) of a number is the number obtained by adding all the digits then adding the digits of that number and then continuing until a single-digit The last two digits of a star number in base 10 are always 01, 13, 21, 33, 37, 41, 53, 61, 73, 81, or 93.

Not many star numbers are also triangular numbers. A triangular number is the sum of the n Natural numbers from 1 to n. 1 and 253 are the only two such numbers in the list given above.

Not many star numbers are also square. 1 and 121 are the only two such numbers in the list given above. Square star numbers can be searched for with the Diophantine equation $2 x 2 + 1 = 3 y 2 . In Mathematics, a Diophantine equation is an indeterminate Polynomial Equation that allows the variables to be Integers only$

All star numbers can be constructed by multiplying a triangular number by 12 and adding one. Hence, all star numbers are odd.

Confusingly, the term "star number" or "stellate number" is occasionally used to refer to octagonal numbers. An octagonal number is a Figurate number that represents an Octagon.

A star prime is a star number that is prime. In Mathematics, a prime number (or a prime) is a Natural number which has exactly two distinct natural number Divisors 1 The first few star primes (sequence A083577 in OEIS) are

13, 37, 73, 181, 337, 433, 541, 661, 937. The On-Line Encyclopedia of Integer Sequences ( OEIS) also cited simply as Sloane's, is an extensive searchable Database of Integer sequences

See also