A024639 n written in fractional base 7/2.

0, 1, 2, 3, 4, 5, 6, 20, 21, 22, 23, 24, 25, 26, 40, 41, 42, 43, 44, 45, 46, 60, 61, 62, 63, 64, 65, 66, 210, 211, 212, 213, 214, 215, 216, 230, 231, 232, 233, 234, 235, 236, 250, 251, 252, 253, 254, 255, 256, 400, 401, 402, 403, 404, 405, 406, 420, 421, 422, 423, 424, 425

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• base
• easy

Comments

To represent a number in base 7, if a digit exceeds 6, subtract 7 and carry 1. In the fractional base 7/2, subtract 7 and carry 2.

Examples

			From _Alonso del Arte_, Apr 21 2019: (Start)
The integers 0 through 6 are written with the digits 0 through 6.
Then, since b = 7/2 is written as 10, and 7 is twice 7/2, 7 is 20 in base 7/2, and therefore a(7) = 20.
a(28) = 210 since 2 * (7/2)^2 + 1 * (7/2) = 2 * 49/4 + 1 * 7/2 = 98/4 + 14/4 = 112/4 = 28. (End)
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to fractional bases.

Crossrefs

Cf. A000079, A000420, A007093, A245342.

Programs

Mathematica

Select[Table[FromDigits[IntegerDigits[n, 7]], {n, 0, 230}], IntegerQ[FromDigits[IntegerDigits[#], 7/2]] &] (* Alonso del Arte, Apr 21 2019 *)
a[n_] := a[n] = If[n == 0, 0, 10 * a[2 * Floor[n/7]] + Mod[n, 7]]; Array[a, 50, 0] (* Amiram Eldar, Jul 31 2025 *)

PARI

a(n) = if(n == 0, 0, 10 * a(n\7 * 2) + n % 7); \\ Amiram Eldar, Jul 31 2025