A245352 Sum of digits of n written in fractional base 7/5.

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

Offset

0,3

Comments

The base 7/5 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(A024642(n)).

Example

In base 7/5 the number 14 is represented by 530 and so a(14) = 5 + 3 + 0 = 8.

Mathematica

a[n_] := a[n] = If[n == 0, 0, a[5 * Floor[n/7]] + Mod[n, 7]]; Array[a, 100, 0] (* Amiram Eldar, Jul 31 2025 *)

Prog

(SageMath) # uses [basepqsum from A245355]
[basepqsum(7, 5, w) for w in [0..200]]
(PARI) a(n) = if(n == 0, 0, a(n\7 * 5) + n % 7); \\ Amiram Eldar, Jul 31 2025

Crossrefs

Cf. A007953, A000120, A244040, A024642, A053828.

Sequence in context: A308973 A309279 A382019 * A099033 A187786 A002330

Adjacent sequences: A245349 A245350 A245351 * A245353 A245354 A245355

Keyword

nonn,base,easy

Author

Hailey R. Olafson, Jul 18 2014

Status

approved