What Is the 10 Digit Autobiographical Number?

What are the facts regarding What Is the 10 Digit Autobiographical Number? Get the answers in this feature article.

… 1210 is the smallest autobiographical number: n = x0x1x2 · x9 such that xi is the number of digits equal to i in n: 1210 is built of one 0, two 1s, and one 2. Martin Gardner in his book ” Mathematical Circus ” [3] gives a puzzle to calculate the only 10-digit autobiographical number.

Are there any autobiographical numbers in the OEIS?

The OEIS, where I first encountered the autobiographical numbers. Autobiographical numbers are very cute numbers. But there is a problem with their name. If there is a notion of an autobiography of a number, then it would be logical to expect that there is a notion of a biography of a number.

What’s the shortest possible biography of a number?

I will call the shortest possible biography of a number the curriculum vitae and the longest possible biography the complete life story. The third problem is that numbers with the same digits in different permutations have the same biographies. So in a sense a biography follows the life not of a number, but rather the set of its digits.