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A233137 Reversed shortest (x+1,2x)-code of n. 4
1, 2, 12, 22, 122, 212, 1212, 222, 1222, 2122, 12122, 2212, 12212, 21212, 121212, 2222, 12222, 21222, 121222, 22122, 122122, 212122, 1212122, 22212, 122212, 212212, 1212212, 221212, 1221212, 2121212, 12121212, 22222, 122222, 212222, 1212222, 221222, 1221222 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

(See A233135.)

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

FORMULA

Define h(x) = x - 1 if x is odd and h(x) = x/2 if x is even, and define H(x,1) = h(x) and H(x,k) = H(H(x,k-1)). For each n > 1, the sequence (H(n,k)) decreases to 1 through two kinds of steps; write 1 when the step is x - 1 and write 2 when the step is x/2. A233137(n) is the concatenation of 1s and 2s, as in the Mathematica program.

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 *)

CROSSREFS

Cf. A040039, A135529, A232559, A000045, A233135, A233136, A233138.

Sequence in context: A108960 A111095 A073211 * A094626 A093378 A012664

Adjacent sequences: A233134 A233135 A233136 * A233138 A233139 A233140

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Dec 05 2013

STATUS

approved

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Last modified February 6 04:04 EST 2023. Contains 360092 sequences. (Running on oeis4.)