A233136 Concatenated shortest (x+1,2x)-codes for the positive integers.

1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1

Offset: 1

Author

Clark Kimberling, Dec 05 2013

Keywords

• nonn
• easy

Comments

Concatenate the representations of the positive integers in A233135, and then separate the digits by commas, in the manner analogous to A030302.

Examples

			A233135 = (1,2,21,22,221,212,...), so that A233136 = (1,2,2,1,2,2,2,2,1,2,1,2,...).
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..2500

Crossrefs

Cf. A040039, A135529, A232559, A000045, A233135, A233137, A233138.

Programs

Mathematica

b[x_] := b[x] = If[OddQ[x], x - 1, x/2]; u[n_] := 2 - Mod[Drop[FixedPointList[b, n], -3], 2]; u[1] = {1}; t = Table[u[n], {n, 1, 30}]; Table[FromDigits[u[n]], {n, 1, 50}]  (* A233137 *)
Flatten[t]  (* A233138 *)
Table[FromDigits[Reverse[u[n]]], {n, 1, 30}]  (* A233135 *)
Flatten[Table[Reverse[u[n]], {n, 1, 30}]]  (* A233136 *)