A092892 Smallest starting value in a Collatz '3x+1' sequence such that the sequence contains exactly n halving steps.

1, 2, 4, 8, 5, 3, 6, 12, 24, 17, 11, 7, 14, 9, 18, 36, 25, 49, 33, 65, 43, 86, 57, 39, 78, 153, 105, 203, 135, 270, 185, 123, 246, 169, 329, 219, 159, 295, 569, 379, 283, 505, 377, 251, 167, 111, 222, 444, 297, 593, 395, 263, 175, 350, 233, 155, 103, 206, 137, 91, 182

Offset

0,2

Comments

First occurrence of n in A006666.

The graph of this sequence has features similar to those of A092893, but with the x-axis scaled by log(3)/log(2). - T. D. Noe, Apr 09 2007

Links

T. D. Noe, Table of n, a(n) for n=0..500

Eric Weisstein's World of Mathematics, Collatz Problem.

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

Example

a(5)=3 because the Collatz sequence 3,10,5,16,8,4,2,1 is the first sequence containing 5 halving steps.

Mathematica

coll[n_]:= NestWhileList[If[EvenQ[#], #/2, 3#+1] &, n, #>1 &]; Table[i = 1; While[Count[coll[i], _?EvenQ] != n, i++]; i, {n, 0, 60}] (* Jayanta Basu, Jun 05 2013 *)

Prog

(Haskell)
import Data.List (elemIndex); import Data.Maybe (fromJust)
a092892 = (+ 1) . fromJust . (`elemIndex` a006666_list)
-- Reinhard Zumkeller, Mar 14 2014

Crossrefs

Cf. A006666, A092893.

Sequence in context: A135447 A163339 A364611 * A146079 A165669 A227818

Adjacent sequences: A092889 A092890 A092891 * A092893 A092894 A092895

Keyword

nonn,look

Author

Hugo Pfoertner, Mar 11 2004

Status

approved