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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 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 the Diophantine Equation 2x^2 + 1 = 3y^2

All star numbers can be constructed by multiplying a triangular number by 12 and adding one.

Confusingly, the term "star number" or "stellate number" is occasionally used to refer to Octagonal Number s.


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