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.
Read more about this topic: Self Number
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