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

1,2

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

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A105776, A108571, A247700.

Sequence in context: A207147 A222578 A105983 * A099154 A304605 A158131

Adjacent sequences: A356366 A356367 A356368 * A356370 A356371 A356372

Keyword

nonn,base,fini

Author

Marc Morgenegg, Oct 17 2022

Extensions

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

Status

approved