Self Number - Recurrent Formula

Recurrent Formula

The following recurrence relation generates some base 10 self numbers:

(with C₁ = 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 C₁ = b − 1 for even bases and C₁ = b − 2 for odd bases.

The existence of these recurrence relations shows that for any base there are infinitely many self numbers.