A245344 Sum of digits of n written in fractional base 7/3.

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

Offset: 0

Author

James Van Alstine, Jul 18 2014

Keywords

• nonn
• base
• easy

Comments

The base 7/3 expansion is unique, and thus the sum of digits function is well-defined.

Examples

			In base 7/3 the number 7 is represented by 30 and so a(7) = 3 + 0 = 3.
		

Links

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

Crossrefs

Cf. A007953, A024640, A053828, A007953.

Programs

Maple

a:= proc(n) `if`(n<1, 0, irem(n, 7, 'q')+a(3*q)) end:
seq(a(n), n=0..69);  # Alois P. Heinz, May 14 2021

Mathematica

a[n_] := a[n] = If[n == 0, 0, a[3 * Floor[n/7]] + Mod[n, 7]]; Array[a, 100, 0] (* Amiram Eldar, Aug 02 2025 *)

PARI

a(n) = if(n == 0, 0, a(n\7 * 3) + n % 7); \\ Amiram Eldar, Aug 02 2025

Sage

# uses [basepqsum from A245355]
[basepqsum(7,3,y) for y in [0..200]]

Formula

a(n) = A007953(A024640(n)). - Amiram Eldar, Aug 02 2025

Extensions

Definition corrected by Georg Fischer, May 14 2021