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

1,2

Comments

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

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (11,-10).

Formula

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

G.f.: x*(1 + 9*x - 100*x^2 + 1090*x^3 - 1900*x^4)/((1 - x)*(1 - 10*x)). - Andrew Howroyd, Nov 13 2025

Example

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

Mathematica

LinearRecurrence[{11, -10}, {1, 20, 110, 2100, 20100}, 20] (* Paolo Xausa, Nov 13 2025 *)

Prog

(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
(PARI) a(n) = if(n < 4, [1, 20, 110][n], 2*10^(n-1) + 100) \\ Andrew Howroyd, Nov 13 2025

Crossrefs

Cf. A046043.

Sequence in context: A008383 A384334 A024192 * A309781 A228243 A086605

Adjacent sequences: A380982 A380983 A380984 * A380986 A380987 A380988

Keyword

nonn,easy,base

Author

Leo Crabbe, Feb 11 2025

Status

approved