A024653 -id:A024653 - cp's OEIS frontend

A245430 Number of nonnegative integers with property that their base 9/5 expansion (see A024653) has n digits.

9, 9, 18, 36, 63, 108, 198, 360, 648, 1161, 2088, 3762, 6768, 12186, 21933, 39483, 71064, 127917, 230256, 414459, 746028, 1342845, 2417121, 4350816, 7831476, 14096655, 25373979, 45673164, 82211688, 147981042, 266365872, 479458575, 863025435, 1553445783, 2796202404

Offset: 1

Tom Edgar, Jul 21 2014

			The numbers 9-17 are represented by  50, 51, 52, 53, 54, 55, 56, 57, 58 respectively in base 9/5. Since these are the only two digit integers we have a(2) = 9.

Cf. A024653, A245356, A081848.

A=[1]
for i in [1..100]:
    A.append(ceil(((9-5)/5)*sum(A)))
[9*x for x in A]

A245354 Sum of digits of n in fractional base 9/5.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 10, 11, 12, 13, 6, 7, 8, 9, 10, 11, 12, 13, 14, 11, 12, 13, 14, 15, 16, 17, 18, 19, 8, 9, 10, 11, 12, 13, 14, 15, 16, 13, 14, 15, 16, 17, 18, 19, 20, 21, 14, 15, 16, 17, 18, 19, 20, 21, 22, 19, 20, 21, 22, 23

Offset: 0

James Van Alstine, Jul 18 2014

The base 9/5 expansion is unique, and thus the sum of digits function is well-defined.

			In base 9/5 the number 11 is represented by 52 and so a(11) = 5 + 2 = 7.

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

Cf. A007953, A024653, A053830.

a[n_] := a[n] = If[n == 0, 0, a[4 * Floor[n/9]] + Mod[n, 9]]; Array[a, 100, 0] (* Amiram Eldar, Aug 02 2025 *)

a(n) = if(n == 0, 0, a(n\9 * 4) + n % 9); \\ Amiram Eldar, Aug 02 2025

# uses [basepqsum from A245355]
[basepqsum(9,5,y) for y in [0..200]]

a(n) = A007953(A024653(n)). - Amiram Eldar, Aug 02 2025

cp's OEIS Frontend

A245430 Number of nonnegative integers with property that their base 9/5 expansion (see A024653) has n digits.

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A245354 Sum of digits of n in fractional base 9/5.

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