| Self Number |
Article Index for Self |
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Information AboutSelf Number |
| CATEGORIES ABOUT SELF NUMBER | |
| base-dependent integer sequences | |
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The first few base 10 self numbers are 1 , 3 , 5 , 7 , 9 , 20 , 31 , 42 , 53 , 64 , 75 , 86 , 97 , 108 , 110 , 121 , 132 , 143 , 154 , 165, 176, 187, 198, 209, 211, 222 , 233 , 244, 255 , 266, 277, 288, 299, 310, 312, 323, 334, 345, 356, 367, 378, 389, 400 , 411, 413, 424, 435, 446, 457, 468, 479, 490, 501, 512, 514, 525 In general, for even bases, all Odd numbers below the base number are self numbers, since any number below such an odd number would have to also be a 1-digit number which when added to its digit would result in an even number. For odd bases, all odd numbers are self numbers. The following Recurrence Relation generates Base 10 self numbers: (with ''C''1 = 9) And for Binary numbers: (where ''j'' stands for the number of digits) we can generalize a recurrence relation to generate self numbers in any base ''b'': in which ''C''1 = ''b'' - 1 for even bases and ''C''1 = ''b'' - 2 for odd bases. The existence of these recurrence relations shows that for any base there are infinitely many self numbers. A search for self numbers can turn up Self-descriptive Number s, which are similar to self numbers in being base-dependent, but quite different in definition and much fewer in frequency. |
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