Star number

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a star number is a <a href="/facts/Centered_number/FAB00ppP">centered</a> <a href="/facts/Figurate_number/f1gdGcja">figurate number</a>, a centered <a href="/facts/Hexagram/IF4PEJbL">hexagram</a> (six-pointed star), such as the <a href="/facts/Star_of_David/L681snpQ">Star of David</a>, or the board <a href="/facts/Chinese_checkers/BabnP6gC">Chinese checkers</a> is played on.
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<table><tbody><tr><th>1</th><th></th><th>13</th><th></th><th>37</th></tr><tr><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>
<p>The <i>n</i>th star number is given by the formula <i>Sn</i> = 6<i>n</i>(<i>n</i> − 1) + 1. The first 45 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, 11353, and 11881. (sequence A003154 in the <a href="/facts/On-Line_Encyclopedia_of_Integer_Sequences/yow6cVsU">OEIS</a>)
</p><p>The <a href="/facts/Digital_root/VeYjMlKY">digital root</a> 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.
</p><p>Unique among the star numbers is 35113, since its prime factors (i.e., 13, 37 and 73) are also consecutive star numbers.
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Star number open-in-new

Star number