A245346 Sum of digits of n in fractional base 10/3.

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

Offset: 0

Author

James Van Alstine, Jul 18 2014

Keywords

• nonn
• base
• easy

Comments

The base 10/3 expansion is unique, and thus the sum of digits function is well-defined.

Examples

			In base 10/3 the number 11 is represented by 31 and so a(11) = 3 + 1 = 4.
		

Links

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

Crossrefs

Cf. A007953, A024658.

Programs

Mathematica

a[n_] := a[n] = If[n == 0, 0, a[3 * 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 * 3) + n % 10); \\ Amiram Eldar, Aug 04 2025

Sage

# uses [basepqsum from A245355]
[basepqsum(10,3,y) for y in [0..200]]

Formula

a(n) = A007953(A024658(n)). - Amiram Eldar, Aug 04 2025