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

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

Author

James Van Alstine, Jul 18 2014

Keywords

• nonn
• base
• easy

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A007953, A024653, A053830.

Programs

Mathematica

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 *)

PARI

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

Sage

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

Formula

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