- Star number
A star number is a centered
figurate number that represents a centeredhexagram , such as the one thatChinese checkers is played on.The "n"th star number is given by the formula 6"n"("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 OEIS|id=A003154.
Geometrically, the "n"th 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 "n"th centred dodecagonal number, but differently arranged.The
digital root of a star number is always 1 or 4. 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 number s. 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 theDiophantine equation 2x^2 + 1 = 3y^2.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 number s.A star prime is a star number that is prime. The first few star primes OEIS|id=A083577 are
13, 37, 73, 181, 337, 433, 541, 661, 937.
ee also
*
centered hexagonal number
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