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Star number
Centered figurate number / From Wikipedia, the free encyclopedia
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A star number is a centered figurate number, a centered hexagram (six-pointed star), such as the Star of David, or the board Chinese checkers is played on.
1 | 13 | 37 | ||
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![]() First four star numbers, by color. | |
Total no. of terms | infinity |
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Formula | |
First terms | 1, 13, 37, 73, 121, 181 |
OEIS index |
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![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/0/08/Chinese_checkers_start.svg/320px-Chinese_checkers_start.svg.png)
The nth star number is given by the formula Sn = 6n(n ā 1) + 1. The first 43 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 the OEIS)
The digital root of a star number is always 1 or 4, and progresses in the sequence 1, 4, 1. 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.
Unique among the star numbers is 35113, since its prime factors (i.e., 13, 37 and 73) are also consecutive star numbers.