A356369 Numbers such that each digit "d" occurs d times, for every digit from 1 to the largest digit.

1, 122, 212, 221, 122333, 123233, 123323, 123332, 132233, 132323, 132332, 133223, 133232, 133322, 212333, 213233, 213323, 213332, 221333, 223133, 223313, 223331, 231233, 231323, 231332, 232133, 232313, 232331, 233123, 233132, 233213, 233231, 233312, 233321, 312233, 312323

Offset: 1

Author

Marc Morgenegg, Oct 17 2022

Keywords

• nonn
• base
• fini

Comments

A version of self-describing integers (cf. A105776).

The sequence is finite.

The last term is 999999999888888887777777666666555554444333221.

This sequence contains Sum_{m = 1..9} Product_{k = 1..m} binomial( k*(k+1)/2, k) = 65191584768311709900058498136517664 terms. - Thomas Scheuerle and David A. Corneth, Oct 17 2022

Examples

			213323 is a term because the digit 1 occurs once, the digit 2 twice and 3 three times. Every digit from 1 to 3 is present.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A105776, A108571, A247700.

Programs

Python

from itertools import islice
from sympy.utilities.iterables import multiset_permutations
def agen():
    for m in range(1, 10):
        s = "".join(str(k)*k for k in range(1, m+1))
        yield from (int("".join(p)) for p in multiset_permutations(s))
print(list(islice(agen(), 65))) # Michael S. Branicky, Oct 17 2022

Extensions

Corrected by and more terms from David A. Corneth, Oct 17 2022