A245336 Sum of digits of n written in fractional base 8/7.

0, 1, 2, 3, 4, 5, 6, 7, 7, 8, 9, 10, 11, 12, 13, 14, 13, 14, 15, 16, 17, 18, 19, 20, 18, 19, 20, 21, 22, 23, 24, 25, 22, 23, 24, 25, 26, 27, 28, 29, 25, 26, 27, 28, 29, 30, 31, 32, 27, 28, 29, 30, 31, 32, 33, 34, 28, 29, 30, 31, 32, 33, 34, 35, 28, 29, 30, 31

Offset

0,3

Comments

The base 8/7 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(A024649(n)).

Example

In base 8/7 the number 14 is represented by 76 and so a(14) = 7 + 6 = 13.

Mathematica

a[n_] := a[n] = If[n == 0, 0, a[7 * Floor[n/8]] + Mod[n, 8]]; Array[a, 100, 0] (* Amiram Eldar, Aug 02 2025 *)

Prog

(SageMath) # uses [basepqsum from A245355]
[basepqsum(8, 7, w) for w in [0..200]]
(PARI) a(n) = if(n == 0, 0, a(n\8 * 7) + n % 8); \\ Amiram Eldar, Aug 02 2025

Crossrefs

Cf. A000120, A007953, A024649, A053829, A244040.

Sequence in context: A227394 A209900 A097043 * A356964 A053759 A060431

Adjacent sequences: A245333 A245334 A245335 * A245337 A245338 A245339

Keyword

nonn,base,easy

Author

Hailey R. Olafson, Jul 18 2014

Status

approved