A024643 n written in fractional base 7/6.

0, 1, 2, 3, 4, 5, 6, 60, 61, 62, 63, 64, 65, 66, 650, 651, 652, 653, 654, 655, 656, 6540, 6541, 6542, 6543, 6544, 6545, 6546, 65430, 65431, 65432, 65433, 65434, 65435, 65436, 654320, 654321, 654322, 654323, 654324, 654325, 654326, 6543210, 6543211, 6543212, 6543213, 6543214, 6543215, 6543216, 65432100, 65432101, 65432102, 65432103, 65432104, 65432105, 65432106, 65432160

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• base
• easy

Comments

To represent a number in base b, if a digit is >= b, subtract b and carry 1. In fractional base a/b, subtract a and carry b.

Examples

			From _Petros Hadjicostas_, Jul 22 2020: (Start)
14 = 6*(7/6)^2 + 5*(7/6)^1 + 0*(7/6)^0 = 650_{7/6}.
15 = 6*(7/6)^2 + 5*(7/6)^1 + 1*(7/6)^0 = 651_{7/6}.
21 = 6*(7/6)^3 + 5*(7/6)^2 + 4*(7/6)^1 + 1*(7/6)^0 = 6541_{7/6}.
22 = 6*(7/6)^3 + 5*(7/6)^2 + 4*(7/6)^1 + 2*(7/6)^0 = 6542_{7/6}.
28 = 6*(7/6)^4 + 5*(7/6)^3 + 4*(7/6)^2 + 3*(7/6)^1 + 0*(7/6)^0 = 65430_{7/6}. (End)
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Index entries for sequences related to fractional bases.

Crossrefs

Cf. A024629, A245337.

Programs

Mathematica

a[n_] := a[n] = If[n == 0, 0, 10 * a[6 * Floor[n/7]] + Mod[n, 7]]; Array[a, 50, 0] (* Amiram Eldar, Jul 31 2025 *)

PARI

a(n) = {if(n<1, 0, a(n\7 * 6) * 10 + n%7)}; \\ Andrew Howroyd, Aug 19 2019

Extensions

Terms a(44) and beyond from Andrew Howroyd, Aug 19 2019