A024656 -id:A024656 - cp's OEIS frontend

A245400 Number of nonnegative integers with property that their base 9/8 expansion (see A024656) has n digits.

9, 9, 9, 9, 9, 9, 9, 9, 9, 18, 18, 18, 18, 27, 27, 27, 36, 36, 45, 45, 54, 63, 72, 81, 90, 99, 108, 126, 144, 162, 180, 198, 225, 252, 288, 324, 360, 405, 459, 513, 576, 648, 729, 819, 927, 1044, 1170, 1314, 1485, 1665, 1872, 2106, 2376, 2673, 3006, 3384, 3807

Offset: 1

Tom Edgar, Jul 21 2014

			a(2) = 9 since 80, 81, 82, 83, 84, 85, 86, 87, 88 are the base 9/8 representations of 9-17 respectively and these are the only integers with 2 digits.

Cf. A245356, A120194, A024656, A081848.

A=[1]
for i in [1..100]:
    A.append(ceil(((9-8)/8)*sum(A)))
[9*x for x in A]

a(n) = 9*A120194(n).

A245338 Sum of digits of n written in fractional base 9/8.

Original entry on oeis.org

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

Offset: 0

Tom Edgar, Jul 18 2014

The base 9/8 expansion is unique and thus the sum of digits function is well-defined.

			In base 9/8 the number 16 is represented by 87 and so a(16) = 8 + 7 = 15.

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

Cf. A000120, A007953, A024656, A053830, A244040.

a[n_] := a[n] = If[n == 0, 0, a[8 * Floor[n/9]] + Mod[n, 9]]; Array[a, 100, 0] (* Amiram Eldar, Aug 04 2025 *)

a(n) = if(n == 0, 0, a(n\9 * 8) + n % 9); \\ Amiram Eldar, Aug 04 2025

# uses [basepqsum from A245355]
[basepqsum(9,8,i) for i in [0..100]]

a(n) = A007953(A024656(n)).

cp's OEIS Frontend

A245400 Number of nonnegative integers with property that their base 9/8 expansion (see A024656) has n digits.

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A245338 Sum of digits of n written in fractional base 9/8.

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