A245341 Sum of digits of n written in fractional base 5/2.

0, 1, 2, 3, 4, 2, 3, 4, 5, 6, 4, 5, 6, 7, 8, 3, 4, 5, 6, 7, 5, 6, 7, 8, 9, 4, 5, 6, 7, 8, 6, 7, 8, 9, 10, 8, 9, 10, 11, 12, 4, 5, 6, 7, 8, 6, 7, 8, 9, 10, 5, 6, 7, 8, 9, 7, 8, 9, 10, 11, 9, 10, 11, 12, 13, 5, 6, 7, 8, 9, 7, 8, 9, 10, 11, 6, 7, 8, 9, 10, 8, 9

Offset: 0

Author

James Van Alstine, Jul 18 2014

Keywords

• nonn
• base
• easy

Comments

The base 5/2 expansion is unique and thus the sum of digits function is well-defined.

Examples

			In base 5/2 the number 7 is represented by 22 and so a(7) = 2+2 = 4.
		

Links

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

Crossrefs

Cf. A024632, A007953, A053824, A215088.

Programs

Maple

a:= proc(n) `if`(n<1, 0, irem(n, 5, 'q')+a(2*q)) end:
seq(a(n), n=0..81);  # Alois P. Heinz, May 14 2021

Mathematica

a[n_] := a[n] = If[n == 0, 0, a[2 * 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 * 2) + n % 5); \\ Amiram Eldar, Jul 30 2025

Sage

# uses [basepqsum from A245355]
[basepqsum(5,2,y) for y in [0..200]]

Formula

a(n) = A007953(A024632(n)). - Amiram Eldar, Jul 30 2025

Extensions

Definition corrected by Georg Fischer, May 14 2021