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

Author

Hugo Pfoertner, Mar 11 2004

Keywords

• nonn
• look

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

Examples

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

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

Crossrefs

Cf. A006666, A092893.

Programs

Haskell

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

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 *)