A024664 -id:A024664 - cp's OEIS frontend

A245403 Number of nonnegative integers with property that their base 10/9 expansion (see A024664) has n digits.

10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 20, 20, 20, 20, 20, 30, 30, 30, 40, 40, 50, 50, 60, 60, 70, 80, 90, 100, 110, 120, 130, 150, 160, 180, 200, 220, 250, 280, 310, 340, 380, 420, 470, 520, 580, 640, 710, 790, 880, 980, 1090, 1210, 1340, 1490, 1660

Offset: 1

James Van Alstine, Jul 21 2014

			The numbers 10-19 are represented by 90, 91, 92, 93, 94, 95, 96, 97, 98, 99 respectively in base 10/9. These are the only integers with two digits, and so a(2)=10.

Cf. A024664, A120202, A081848.

A=[1]
for i in [1..60]:
    A.append(ceil((10-9)/9*sum(A)))
[10*x for x in A]

a(n) = 10*A120202(n).

A245339 Sum of digits of n written in fractional base 10/9.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 39, 40, 41, 42, 43, 44, 45, 46

Offset: 0

Hailey R. Olafson, Jul 18 2014

The base 10/9 expansion is unique and thus the sum of digits function is well-defined.

			In base 10/9 the number 14 is represented by 94 and so a(14) = 9 + 4 = 13.

Amiram Eldar, Table of n, a(n) for n = 0..10000
Index entries for sequences related to fractional bases.

Cf. A000120, A007953, A024664, A244040.

a[n_] := a[n] = If[n == 0, 0, a[9 * Floor[n/10]] + Mod[n, 10]]; Array[a, 100, 0] (* Amiram Eldar, Aug 04 2025 *)

a(n) = if(n == 0, 0, a(n\10 * 9) + n % 10); \\ Amiram Eldar, Aug 04 2025

# uses [basepqsum from A245355]
[basepqsum(10,9,w) for w in [0..200]]

a(n) = A007953(A024664(n)).

cp's OEIS Frontend

A245403 Number of nonnegative integers with property that their base 10/9 expansion (see A024664) has n digits.

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A245339 Sum of digits of n written in fractional base 10/9.

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