Star number

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A star number, or centered 12-gonal number, is a centered figurate number that represents a centered hexagram, such as the one that Chinese checkers are played on. The star numbers for n 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

The digital root of a star number is always 1 or 4. The last two digits of a star number are always 01, 13, 21, 33, 37, 41, 53, 61, 73, 81, or 93.

Not many star numbers are also triangular numbers. 1 and 253 are the only two such numbers in the list given above.

Also, not many star numbers are also square, with 1 and 121 being the only two such numbers in the list given above. Square star numbers can be searched for with the Diophantine equation

<math>2x^2 + 1 = 3y^2<math>

See also: centered hexagonal number