A245350 Sum of digits of n written in fractional base 9/4.

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

Offset

0,3

Comments

The base 9/4 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(A024652(n)).

Example

In base 9/4 the number 16 is represented by 47 and so a(16) = 4 + 7 = 11.

Mathematica

a[n_] := a[n] = If[n == 0, 0, a[4 * Floor[n/9]] + Mod[n, 9]]; Array[a, 100, 0] (* Amiram Eldar, Aug 02 2025 *)

Prog

(SageMath) # uses [basepqsum from A245355]
[basepqsum(9, 4, i) for i in [0..100]]
(PARI) a(n) = if(n == 0, 0, a(n\9 * 4) + n % 9); \\ Amiram Eldar, Aug 02 2025

Crossrefs

Cf. A000120, A007953, A024652, A053830, A244040.

Sequence in context: A282779 A327535 A305902 * A307282 A245354 A382725

Adjacent sequences: A245347 A245348 A245349 * A245351 A245352 A245353

Keyword

nonn,base,easy

Author

Tom Edgar, Jul 18 2014

Status

approved