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