| Centered Octagonal Number |
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: where ''T'' is a regular Triangular Number , or much more simply, by squaring the odd numbers: : The first few centered octagonal numbers are 1 , 9 , 25 , 49 , 81 , 121 , 169 , 225, 289, 361, 441, 529, 625, 729, 841, 961 All centered octagonal numbers are odd, and in base 10 one can notice the one's digits follow the pattern 1-9-5-9-1. Calculating Ramanujan's Tau Function on a centered octagonal number yields an odd number, whereas for any other number the function yields an even number. See also regular Octagonal Number . |
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