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, ... In base 12, the self numbers are: (using A and B for ten and eleven, respectively) 1, 3, 5, 7, 9, B, 20, 31, 42, 53, 64, 75, 86, 97, A8, B9, 102, 110, 121, 132, 143, 154, 165, 176, 187, 198, 1A9, 1BA, 20B, 211, 222, 233, 244, 255, 266, 277, 288, 299, 2AA, 2BB, 310, 312, 323, 334, 345, 356, 367, 378, 389, 39A, 3AB, 400, 411, 413, 424, 435, 446, 457, 468, 479, 48A, 49B, 4B0, 501, 512, 514, 525, 536, 547, 558, 569, 57A, 58B, 5A0, 5B1, ... Self primes A self prime is a self number that is prime. The first few self primes in base 10 are 3, 5, 7, 31, 53, 97, 211, 233, 277, 367, 389, 457, 479, 547, 569, 613, 659, 727, 839, 883, 929, 1021, 1087, 1109, 1223, 1289, 1447, 1559, 1627, 1693, 1783, 1873, ... The first few self primes in base 12 are: 3, 5, 7, B, 31, 75, 255, 277, 2AA, 3BA, 435, 457, 58B, 5B1, ... In October 2006 Luke Pebody demonstrated that the largest known Mersenne prime in base 10 that is at the same time a self number is 224036583−1. This is then the largest known self prime in base 10 . Extension to negative integers Self numbers can be extended to the negative integers by use of a signed-digit representation to represent each integer. Excerpt from the table of bases where 2007 is self The following table was calculated in 2007. References Kaprekar, D. R. The Mathematics of New Self-Numbers Devaiali (1963): 19 - 20. Arithmetic dynamics Base-dependent integer sequences Inverse functions