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

0,12

Comments

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).

For a given m >= 1, special cases a(n) = m occur for n in the range k*(A002275(m)-1)+1 <= n <= k*A002275(m) with 1 <= k <= 10 since then 9*n becomes repeat 9's and first digit and last 2 digits summing to 9*m. - Rhys Feltman, Nov 13 2025

Links

Michael S. Branicky, Table of n, a(n) for n = 0..10000

Formula

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).

a(A002275(m)) = m for all m >= 0 and a(k) < m for k < A002275(m), or in other words, m first appears as a term at index A002275(m). - Michael S. Branicky, Nov 25 2025

Mathematica

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

Prog

(PARI) A343639(n)=sumdigits(9*n)/9
(Python)
def a(n): return sum(map(int, str(9*n)))//9
print([a(n) for n in range(112)]) # Michael S. Branicky, Nov 24 2025

Crossrefs

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

Cf. A002264, A002275, A008585, A193582, A326307.

Sequence in context: A184340 A083911 A326307 * A095827 A380706 A193582

Adjacent sequences: A343636 A343637 A343638 * A343640 A343641 A343642

Keyword

nonn,base,easy

Author

M. F. Hasler, May 19 2021

Status

approved