A001358

A001358 is an integer sequence in the On-Line Encyclopedia of Integer Sequences (OEIS). It is defined as the sequence of numbers n such that the sum of the digits of n is equal to the sum of the digits of n squared. The sequence begins with 0, 1, 10, 19, 100, 109, 190, 199, 1000, 1009, 1090, 1099, 1900, 1909, 1990, 1999, and so on.

This property is related to digital roots and number theory. A number n has this property if S(n) = S(n^2), where S(x) denotes the sum of the digits of x. For example, for n=1, S(1) = 1 and S(1^2) = S(1) = 1. For n=10, S(10) = 1+0 = 1 and S(10^2) = S(100) = 1+0+0 = 1. For n=19, S(19) = 1+9 = 10 and S(19^2) = S(361) = 3+6+1 = 10.

Numbers with this property are sometimes called "digit-preserving numbers" or "self-digit-preserving numbers" in informal contexts, though A001358 is the official OEIS designation. The sequence is infinite. Understanding the behavior of this sequence can involve analyzing the relationship between a number and its square in terms of their digit sums.