self number

An integer n that in a given base b lacks a digitaddition generator.

Consider, for example, the integer 41 in base 10. It can be expressed as 34 + 3 + 4. For 42, however, there is no such digitaddition, hence it is a self number.

If 2|b, all odd n<b will be self numbers.

Though self numbers form a small proportion of most ranges of 2b consecutive integers, there are infinitely many of them: The recurrence relation Si=(b-2)bi-1+Si-1+(b-2) (with S1=b-1 if 2|b and S1=b-2 otherwise) will give an incomplete though infiniteMathworldPlanetmath list of self numbers.


Kaprekar, D. R. The Mathematics of New Self-Numbers. Devaiali, 1963: 19 - 20

Title self number
Canonical name SelfNumber
Date of creation 2013-03-22 15:56:15
Last modified on 2013-03-22 15:56:15
Owner CompositeFan (12809)
Last modified by CompositeFan (12809)
Numerical id 6
Author CompositeFan (12809)
Entry type Definition
Classification msc 11A63
Synonym Columbian number
Synonym Colombian number
Synonym self-number