A245347 Sum of digits of n written in fractional base 8/3.

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

Offset: 0

Author

Hailey R. Olafson, Jul 18 2014

Keywords

• nonn
• base
• easy

Comments

The base 8/3 expansion is unique and thus the sum of digits function is well-defined.

Examples

			In base 8/3 the number 14 is represented by 36 and so a(14) = 3 + 6 = 9.
		

Links

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

Crossrefs

Cf. A000120, A007953, A024645, A053829, A244040.

Programs

Mathematica

a[n_] := a[n] = If[n == 0, 0, a[3 * Floor[n/8]] + Mod[n, 8]]; Array[a, 100, 0] (* Amiram Eldar, Aug 02 2025 *)

PARI

a(n) = if(n == 0, 0, a(n\8 * 3) + n % 8); \\ Amiram Eldar, Aug 02 2025

Sage

# uses [basepqsum from A245355]
[basepqsum(8,3,w) for w in [0..200]]

Formula

a(n) = A007953(A024645(n)).