A245343 Sum of digits of n written in fractional base 5/3.

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

Offset: 0

Author

James Van Alstine, Jul 18 2014

Keywords

• nonn
• base
• easy

Comments

The base 5/3 expansion is unique and thus the sum of digits function is well-defined.

Examples

			In base 5/3 the number 7 is represented by 32 and so a(7) = 3+2 = 5.
		

Links

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

Crossrefs

Cf. A024633, A007953, A053824.

Programs

Mathematica

a[n_] := a[n] = If[n == 0, 0, a[3 * Floor[n/5]] + Mod[n, 5]]; Array[a, 100, 0] (* Amiram Eldar, Jul 30 2025 *)

PARI

a(n) = if(n == 0, 0, a(n\5 * 3) + n % 5); \\ Amiram Eldar, Jul 30 2025

Sage

# uses [basepqsum from A245355]
[basepqsum(5,3,y) for y in [0..200]]

Formula

a(n) = A007953(A024633(n)). - Amiram Eldar, Jul 30 2025

Extensions

Name corrected by Bernard Schott, Mar 18 2020