osanumero

Osanumero is a term used in some puzzle and recreational mathematics circles to refer to self-descriptive numbers, that is, numbers whose digits describe the counts of digits within their own representation. The concept emphasizes self-reference in numeral form and is discussed in the context of base-n representations.

In base b, an osanumero is a sequence of b digits d0, d1, ..., d(b-1) such that for each i, di equals the number of occurrences of the digit i in the entire representation. In other words, the digit at position i records how many times the digit i appears among all digits of the number when written in base b.

Examples in base 10 include 1210 and 2020, which are four-digit numbers that satisfy the condition: for 1210, there is one 0, two 1s, one 2, and zero 3s; for 2020, there are two 0s, zero 1s, two 2s, and zero 3s. A longer, well-known example in base 10 is 6210001000, a ten-digit number where the counts of digits 0 through 9 are 6, 2, 1, 0, 0, 0, 1, 0, 0, 0, respectively.

Osanumero is used mainly for educational and recreational purposes to illustrate self-reference and fixed-point properties of numeral systems. It relates to the broader concept of self-descriptive numbers and autonomic wordplay in digits.

See also: Self-descriptive number; Autogram; Digit inventory.