examples of self numbers in a few selected bases


In base 10, the first few self numbers are 1, 3, 5, 7, 9, 20, 31, 42, 53, 64, 75, 86, 97 (listed in Sloane’s A003052). The recurrence relationMathworldPlanetmath Si=810i-1+Si-1+8 with S1=9 gives the list 9, 97, 905, 8913…

In binary, the first few self numbers are 1, 4, 6, 13, 15, 18, 21, 23, 30, 32, 37, 39, 46, 48, 51, 54 (listed in A010061 of Sloane’s OEIS). The recurrence relation Si=2k+Si-1+1 with S1=1 and k being the number of bits in the number Si-1 has, gives the list 1, 4, 13, 30…

In hexadecimal, the first few self numbers are 1, 3, 5, 7, 9, 11, 13, 15, 32, 49, 66, 83, 100, 117, 134 (not currently listed in the OEIS). The recurrence relation Si=1416i-1+Si-1+14 gives the list 1, 239, 3837, 61195…

In factorial base, the first few self numbers are 1, 4, 11, 18, 36, 43, 61, 68, 86, 93, 111, 118, 125, 132. I don’t know of a recurrence relation that will generate factorial base self numbers.

Lastly, in Roman numerals, the first few self numbers are 1, 3, 5, 7, 8, 9, 11, 13, 15.

Title examples of self numbers in a few selected bases
Canonical name ExamplesOfSelfNumbersInAFewSelectedBases
Date of creation 2013-03-22 15:56:18
Last modified on 2013-03-22 15:56:18
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 5
Author PrimeFan (13766)
Entry type Example
Classification msc 11A63