A245335 Sum of digits of n in fractional base 5/4.

0, 1, 2, 3, 4, 4, 5, 6, 7, 8, 7, 8, 9, 10, 11, 9, 10, 11, 12, 13, 10, 11, 12, 13, 14, 10, 11, 12, 13, 14, 14, 15, 16, 17, 18, 13, 14, 15, 16, 17, 16, 17, 18, 19, 20, 14, 15, 16, 17, 18, 16, 17, 18, 19, 20, 20, 21, 22, 23, 24, 17, 18, 19, 20, 21, 18, 19, 20, 21

Offset: 0

Author

James Van Alstine, Jul 18 2014

Keywords

• nonn
• base
• easy

Comments

The base 5/4 expansion is unique and thus the sum of digits function is well-defined.

Examples

			In base 5/4 the number 7 is represented by 42 and so a(7) = 4+2 = 6.
		

Links

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

Crossrefs

Cf. A024634, A007953, A053824.

Programs

Mathematica

a[n_] := a[n] = If[n == 0, 0, a[4 * Floor[n/5]] + Mod[n, 5]]; Array[a, 100, 0] (* Amiram Eldar, Jul 31 2025 *)

PARI

a(n) = my(ret=0,r); while(n, [n,r]=divrem(n,5); ret+=r; n<<=2); ret; \\ Kevin Ryde, Aug 11 2023

Sage

# uses [basepqsum from A245355]
[basepqsum(5,4,y) for y in [0..200]]

Formula

a(n) = A007953(A024634(n)). - Kevin Ryde, Aug 11 2023