Self-descriptive number: d-digit number where digit at position i (0-indexed) counts occurrences of digit i. Base 10: 6210001000 is the only one. Base 4: 1210, 2020. Base 5: 21200. Each base b≥4 has exactly one: (b−4)·b^(b−1) + 2·b^(b−2) + b^(b−3) + b^0.
How to Use
Enter number:
- Self-desc?: Verify property
- Analysis: Digit-by-digit check
- Base: Try different bases
General Formula
In base b (b≥7): the unique self-descriptive number is (b−4)0...0210...001 — digit 0 is b−4, digit 1 is 2, digit 2 is 1, digit b−4 is 1, rest 0. For b=4,5,6: slightly different.
Related Concepts
- Autobiographical numbers: same idea
- Curious numbers: other self-referential properties
- Look-and-say sequence: describes previous term
Step-by-Step Instructions
- 1Enter number.
- 2Check self-descriptive.
- 3See analysis.
- 4Try other bases.