A326307 -id:A326307 - cp's OEIS frontend

A343639 a(n) = (Sum of digits of 9*n) / 9.

0, 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, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 0

M. F. Hasler, May 19 2021

Similar to, but different from A193582, A326307, ...

Consider g = A008585 = multiply by 3, and its left inverse h = A002264, h o g = id (but g o h = id only on (the range of) A008585). In the spirit of group theory, we can write ad(g) = (x -> h o x o g), then A343638 = ad(A008585)(A007953) and this A343639 = ad(A008585)(A343638) = ad(A008585)^2 (A007953).

Cf. A007953 (digit sum), A008591 (9n), A343638 (similar for 3), A083824 (9*n reversed and divided by 9), A279777 (a(n)=3).

a[n_] := Plus @@ IntegerDigits[9*n]/9; Array[a, 100, 0] (* Amiram Eldar, May 19 2021 *)

PARI
```
A343639(n)=sumdigits(9*n)/9
```

a(n) = A007953(A008591(n))/9, by definition. - Felix Fröhlich, May 19 2021

a(n) = A343638(3*n)/3 = A002264(A343638(A008585(n))), i.e., A343639 = A002264 o A343638 o A008585 (just as A343638 = A002264 o A007953 o A008585).

A380706 n is the a(n)-th nonnegative integer having its set of decimal digits.

Original entry on oeis.org

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, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 1, 1, 1

Offset: 0

Alois P. Heinz, Jan 30 2025

Different from A326307.

			a(101) = 3 because 101 is the 3rd nonnegative integer having its set of decimal digits: 10, 100, 101: {0,1}.

Alois P. Heinz, Table of n, a(n) for n = 0..65536

Cf. A326307 (the same for multiset).

p:= proc() 0 end:
a:= proc(n) option remember; local t;
      t:= {convert(n, base, 10)[]}; p(t):= p(t)+1
    end:
seq(a(n), n=0..105);

from collections import Counter
from itertools import count, islice
def agen(): # generator of terms
    digsetcount = Counter()
    for n in count(0):
        key = "".join(sorted(set(str(n))))
        digsetcount[key] += 1
        yield digsetcount[key]
print(list(islice(agen(), 106))) # Michael S. Branicky, Jan 30 2025

cp's OEIS Frontend

A343639 a(n) = (Sum of digits of 9*n) / 9.

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A380706 n is the a(n)-th nonnegative integer having its set of decimal digits.

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