A245347 Sum of digits of n written in fractional base 8/3.

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

Offset

0,3

Comments

The base 8/3 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(A024645(n)).

Example

In base 8/3 the number 14 is represented by 36 and so a(14) = 3 + 6 = 9.

Mathematica

a[n_] := a[n] = If[n == 0, 0, a[3 * Floor[n/8]] + Mod[n, 8]]; Array[a, 100, 0] (* Amiram Eldar, Aug 02 2025 *)

Prog

(SageMath) # uses [basepqsum from A245355]
[basepqsum(8, 3, w) for w in [0..200]]
(PARI) a(n) = if(n == 0, 0, a(n\8 * 3) + n % 8); \\ Amiram Eldar, Aug 02 2025

Crossrefs

Cf. A000120, A007953, A024645, A053829, A244040.

Sequence in context: A071074 A279648 A066323 * A278059 A329606 A115871

Adjacent sequences: A245344 A245345 A245346 * A245348 A245349 A245350

Keyword

nonn,base,easy

Author

Hailey R. Olafson, Jul 18 2014

Status

approved