A125711 In the "3x+1" problem, let 1 denote a halving step and 0 denote an x->3x+1 step. Then a(n) is obtained by writing the sequence of steps needed to reach 1 from 2n and reading it as a decimal number.

1, 3, 175, 7, 47, 431, 87791, 15, 743151, 111, 22255, 943, 751, 218863, 175087, 31, 5871, 1791727, 1431279, 239, 191, 55023, 44015, 1967, 11917039, 1775, 3515647479163389605506303638875119, 481007, 382703, 437231, 108202665749908974283165422824431, 63, 95803119

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Index entries for sequences related to 3x+1 (or Collatz) problem

Example

6 -> 3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1, so a(3) is the decimal equivalent of 10101111, which is 175.

Maple

b:= proc(n) option remember; `if`(n=1, [0$2], `if`(n::even,
     (p-> p+[1, 2^p[1]])(b(n/2)), (p-> p+[1, 0])(b(3*n+1))))
    end:
a:= n-> b(2*n)[2]:
seq(a(n), n=1..33);  # Alois P. Heinz, Apr 02 2025

Mathematica

f[x_] := If[EvenQ[x], x/2, 3x + 1]; g[n_] := FromDigits[Mod[Most[NestWhileList[f, 2n, # > 1 &]], 2, 1] - 1, 2]; Table[g[n], {n, 40}] (* Ray Chandler, Feb 02 2007 *)

Crossrefs

Cf. A006577, A125710, A125626.

Sequence in context: A299304 A299462 A300105 * A268949 A113270 A091324

Adjacent sequences: A125708 A125709 A125710 * A125712 A125713 A125714

Keyword

nonn,look,base

Author

N. J. A. Sloane, Feb 01 2007

Extensions

Extended by Ray Chandler, Feb 02 2007

Status

approved