A245349 Sum of digits of n written in fractional base 7/4.

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

Offset

0,3

Comments

The base 7/4 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(A024641(n)). - Amiram Eldar, Jul 31 2025

Example

In base 7/4 the number 7 is represented by 40 and so a(7) = 4 + 0 = 4.

Mathematica

a[n_] := a[n] = If[n == 0, 0, a[4 * Floor[n/7]] + Mod[n, 7]]; Array[a, 100, 0] (* Amiram Eldar, Jul 31 2025 *)

Prog

(SageMath) # uses [basepqsum from A245355]
[basepqsum(7, 4, y) for y in [0..200]]
(PARI) a(n) = if(n == 0, 0, a(n\7 * 4) + n % 7); \\ Amiram Eldar, Jul 31 2025

Crossrefs

Cf. A024641, A053828, A007953.

Sequence in context: A070667 A391573 A374056 * A122416 A307784 A134665

Adjacent sequences: A245346 A245347 A245348 * A245350 A245351 A245352

Keyword

nonn,base,easy

Author

James Van Alstine, Jul 18 2014

Status

approved