A326307 a(n) is the index of n in the ordered list of the numbers with the same digits as n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2

Offset: 0

Author

David A. Corneth, Oct 17 2019

Keywords

• nonn
• base
• easy
• look

Comments

Ordinal transform of A328447.

Examples

			a(321) = 6 as 321 is the sixth number made of the digits [1, 2, 3]. The five smaller numbers having these digits are 123, 132, 213, 231, 312.
		

Links

• David A. Corneth, Table of n, a(n) for n = 0..9999
• David A. Corneth, PARI program

Crossrefs

Cf. A179239, A254524, A328447.

Programs

PARI

see Corneth link

PARI

{ o = vector(100); for (n=0, 87, print1 (o[1+fromdigits(vecsort(digits(n,base=10),,4),base)]++ ", ")) } \\ Rémy Sigrist, Oct 17 2019

PARI

A326307(n,D=Vecsmall(digits(n)),c=1)={forperm(vecsort(D),d, d==D&&break; d[1]&&c++);c} \\ M. F. Hasler, May 19 2021

Python

from collections import Counter
from itertools import count, islice
def agen(): # generator of terms
    digmultisetcount = Counter()
    for n in count(0):
        key = "".join(sorted(str(n)))
        digmultisetcount[key] += 1
        yield digmultisetcount[key]
print(list(islice(agen(), 88))) # Michael S. Branicky, Jan 30 2025

Formula

a(A179239(n)) = 1.

a(10+n) = A007953(9*n)/9 (A007953 = sum of digits) for 0 < n < 91, but a(101) = 1 while A007953(9*91)/9 = 2. - M. F. Hasler, May 19 2021

Extensions

Edited by N. J. A. Sloane, Oct 24 2019