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

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

Author

Tom Edgar, Jul 18 2014

Keywords

• nonn
• base
• easy

Comments

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

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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 *)

PARI

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

Sage

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

Formula

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