A284668 Numbers that have the largest Collatz total stopping time of all numbers below 10^n. The smallest number is chosen in case of ties.

9, 97, 871, 6171, 77031, 837799, 8400511, 63728127, 670617279, 9780657630, 75128138247, 989345275647, 7887663552367, 80867137596217, 942488749153153, 7579309213675935, 93571393692802302, 931386509544713451

Offset

1,1

Comments

Collatz stopping time is defined as the number of steps that a number n takes to converge to 1 using one of the following steps:

0) if n is 1, stop.

1) if n is even, divide n by 2 (n/2).

2) if n is odd, multiply n by 3 and add 1 (3n+1).

Subsequence of A006877. The first tie occurs at a(10) which is tied with 9780657631. - Jens Kruse Andersen, Feb 23 2021

Links

Table of n, a(n) for n=1..18.

Gary T. Leavens and Mike Vermeulen, 3x+1 Search Programs, Computers & Mathematics with Applications. 24 (11): 79-99 (1992).

Eric Roosendaal, 3x+1 delay records

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

Formula

a(n) = max{i} (steps(i) for i in range from 1 to 10^n-1).

max(i) returns the i with the maximum steps(i) value.

where steps(n) is defined as follows

steps(n)= 0 if n=1.

1+steps(n/2) if n is even.

1+steps(3*n+1) if n is odd.

Example

For n=1, steps(1) to steps(9) take the following values: 0, 1, 7, 2, 5, 8, 16, 3, 19; the maximum of all those is 19 which occurs for steps(9) therefore a(1)=9.

Mathematica

Table[Last@Ordering@Array[If[#>1, #0@If[OddQ@#, 3#+1, #/2]+1, 0]&, 10^k], {k, 4}] (* Giorgos Kalogeropoulos, Apr 01 2021 *)

Prog

(Python 3.4)
def steps(n):
if n==1:
  return 0
else:
  if (n%2)==0:
  return 1+steps(int(n/2))
  else:
  return 1+steps(3*n+1)
def max_steps(i):
    a=max([[i, steps(i)] for i in range(1, 10**(i))], key=lambda x:x[1])
    return a[0]

Crossrefs

Cf. A006577, A006877.

Sequence in context: A158489 A069636 A069621 * A232229 A240780 A236672

Adjacent sequences: A284665 A284666 A284667 * A284669 A284670 A284671

Keyword

nonn

Author

Rahul Chand, Apr 01 2017

Extensions

Clarified and extended by Jens Kruse Andersen, Feb 23 2021

Status

approved