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

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

Author

Hailey R. Olafson, Jul 18 2014

Keywords

• nonn
• base
• easy

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A000120, A007953, A024664, A244040.

Programs

Mathematica

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 *)

PARI

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

Sage

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

Formula

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