A060412 In the '3x+1' problem, these values for the starting value set new records for the "dropping time", number of steps to reach a lower value than the start.

2, 3, 7, 27, 703, 10087, 35655, 270271, 362343, 381727, 626331, 1027431, 1126015, 8088063, 13421671, 20638335, 26716671, 56924955, 63728127, 217740015, 1200991791, 1827397567, 2788008987, 12235060455

Offset

1,1

Comments

The (3x+1)/2 steps and the halving steps are counted. - Don Reble, May 13 2006

Where records occur in A102419 (could be prefixed by an initial 1). - N. J. A. Sloane, Oct 20 2012

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..35 (from the web page of Tomás Oliveira e Silva)

Tomás Oliveira e Silva, Tables

Eric Roosendaal, On the 3x + 1 problem

N. J. A. Sloane, First 36 terms of A217934 and A060412 [From Roosendaal web site]

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

Example

See A102419.

Mathematica

dcoll[n_]:=Length[NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>=n&]]; t={max=2}; Do[If[(y=dcoll[n])>max, max=y; AppendTo[t, n]], {n, 3, 1130000, 4}]; t (* Jayanta Basu, May 28 2013 *)

Crossrefs

A060413 gives associated "dropping times", A060414 the maximal values and A060415 the steps at which the maxima occur. See also A217934.

Cf. A060445, A008884, A161021, A161022, A161023, A014682, A126241.

Sequence in context: A052877 A137075 A270347 * A276665 A062573 A019435

Adjacent sequences: A060409 A060410 A060411 * A060413 A060414 A060415

Keyword

nonn

Author

N. J. A. Sloane, Apr 06 2001; b-file added Nov 27 2007

Status

approved