A100909 Concatenate number of occurrences in n of each decimal digit from 0 to 9 and drop leading zeros.

1000000000, 100000000, 10000000, 1000000, 100000, 10000, 1000, 100, 10, 1, 1100000000, 200000000, 110000000, 101000000, 100100000, 100010000, 100001000, 100000100, 100000010, 100000001, 1010000000, 110000000, 20000000, 11000000, 10100000, 10010000, 10001000

Offset: 0

Author

Rick L. Shepherd, Nov 21 2004

Keywords

• base
• easy
• nonn

Comments

n = 0 is normally represented as the single digit 0, so a(0) = 1000000000. This representation system is inherently ambiguous by disregarding the order of n's digits but without modification will correctly identify those digits for all numbers up to 999999999 decimal; i.e., a(999999999) = 9; and for many beyond (e.g., a(121212121212121212) = a(111222111222222111) = ... = 990000000). However, for any n in which more than 9 of any single digit occur, additional ambiguity is introduced unless some type of grouping is also used (say, parentheses around or bars over a group of consecutive digits when written) so that, for example, (10) is known to represent 9999999999 rather than 8.

Examples

			a(12) = 110000000 as 12 consists only of one 1 and one 2, hence the following are concatenated: 0 1 1 0 0 0 0 0 0 0 and dropping the leading 0 gives 110000000 (= a(21) also).
		

Links

• Mia Boudreau, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A100910 (each number of digit occurrences is a separate term).

Programs

Mathematica

A100909[n_] := FromDigits[RotateRight[DigitCount[n]]];
Array[A100909, 25, 0] (* Paolo Xausa, Jul 16 2025 *)