A024647 n written in fractional base 8/5.

0, 1, 2, 3, 4, 5, 6, 7, 50, 51, 52, 53, 54, 55, 56, 57, 520, 521, 522, 523, 524, 525, 526, 527, 570, 571, 572, 573, 574, 575, 576, 577, 5240, 5241, 5242, 5243, 5244, 5245, 5246, 5247, 5710, 5711, 5712, 5713, 5714, 5715, 5716, 5717, 5760, 5761, 5762, 5763, 5764, 5765

Offset

0,3

Comments

To represent a number in base 8, if a digit exceeds 7, subtract 8 and carry 1. In the fractional base 8/5, subtract 8 and carry 5.

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Index entries for sequences related to fractional bases.

Example

The integers 0 through 7 are written with the digits 0 through 7.
Then, since b = 8/5 is written as 10, and 8 is five times 8/5, 8 is 50 in base 8/5, and therefore a(8) = 50.
a(16) = 520, since 5 * (8/5)^2 + 2 * (8/5) = 5 * 64/25 + 2 * 8/5 = 64/5 + 16/5 = 80/5 = 16.

Mathematica

Select[Table[FromDigits[IntegerDigits[n, 8]], {n, 0, 4095}], IntegerQ[FromDigits[IntegerDigits[#], 8/5]] &] (* Alonso del Arte, Aug 05 2019 *)
a[n_] := a[n] = If[n == 0, 0, 10 * a[5 * Floor[n/8]] + Mod[n, 8]]; Array[a, 50, 0] (* Amiram Eldar, Aug 02 2025 *)

Prog

(PARI) a(n) = if(n == 0, 0, 10 * a(n\8 * 5) + n % 8); \\ Amiram Eldar, Aug 02 2025

Crossrefs

Cf. A245355.

Sequence in context: A084831 A037406 A237344 * A250263 A024648 A004858

Adjacent sequences: A024644 A024645 A024646 * A024648 A024649 A024650

Keyword

nonn,base,easy

Author

David W. Wilson

Status

approved