A380985 Numbers whose k-th digit indicates the number of digits which occur k times.

1, 20, 110, 2100, 20100, 200100, 2000100, 20000100, 200000100, 2000000100, 20000000100, 200000000100, 2000000000100, 20000000000100, 200000000000100, 2000000000000100, 20000000000000100, 200000000000000100, 2000000000000000100, 20000000000000000100

Offset: 1

Author

Leo Crabbe, Feb 11 2025

Keywords

• nonn
• easy
• base

Comments

The most significant digit is digit position k=1, meaning that it counts how many numbers appear 1 time.

Examples

			110 is a term because 1 number appears once (0), 1 number appears twice (1) and 0 numbers appear 3 times.
		

Crossrefs

Cf. A046043.

Programs

Python

from collections import Counter
def ok(n):
    d = list(map(int, str(n)))
    c = Counter(Counter(d).values())
    return all(dk == c[k] for k, dk in enumerate(d, 1)) # Michael S. Branicky, Feb 18 2025

Formula

a(n) = 2*10^(n-1) + 100 for n >= 4. - Andrew Howroyd, Feb 22 2025