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

0,3

Comments

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

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Index entries for sequences related to fractional bases.

Formula

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

Example

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

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 *)

Prog

(SageMath) # uses [basepqsum from A245355]
[basepqsum(5, 4, y) for y in [0..200]]
(PARI) a(n) = my(ret=0, r); while(n, [n, r]=divrem(n, 5); ret+=r; n<<=2); ret; \\ Kevin Ryde, Aug 11 2023

Crossrefs

Cf. A024634, A007953, A053824.

Sequence in context: A195172 A367193 A277425 * A244230 A277814 A006162

Adjacent sequences: A245332 A245333 A245334 * A245336 A245337 A245338

Keyword

nonn,base,easy

Author

James Van Alstine, Jul 18 2014

Status

approved