

A078417


Numbers k such that h(k) = h(k+1), where h(k) is the length of k, f(k), f(f(k)), ..., 1 in the Collatz (or 3x + 1) problem. (The earliest "1" is meant.)


4



12, 14, 18, 20, 22, 28, 29, 34, 36, 37, 44, 45, 49, 50, 52, 54, 60, 62, 65, 66, 68, 69, 76, 78, 82, 84, 86, 92, 94, 98, 99, 100, 101, 108, 109, 114, 116, 118, 124, 125, 130, 131, 132, 133, 140, 142, 145, 146, 148, 150, 156, 157, 162, 164, 165, 172, 173, 177, 178
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OFFSET

1,1


COMMENTS

Recall that f(k) = k/2 if k is even, 3k + 1 if k is odd (A006370).


LINKS

Eric M. Schmidt, Table of n, a(n) for n = 1..10000
Marcus Elia and Amanda Tucker, Consecutive Integers and the Collatz Conjecture, arXiv:1511.09141 [math.NT], 2015.
Lynn E. Garner, On heights in the Collatz 3n+1 problem, Discrete Math, 55 (1985), 5764.
Eric Weisstein's World of Mathematics, Collatz Problem
Wikipedia, Collatz Conjecture
Index entries for sequences related to 3x+1 (or Collatz) problem


EXAMPLE

The Collatz trajectories k, f(k), f(f(k)), ..., 1 for k = 12 and 13, respectively, are {12, 6, 3, 10, 5, 16, 8, 4, 2, 1} and {13, 40, 20, 10, 5, 16, 8, 4, 2, 1}, which are both of length 10. Hence h(12) = h(13) = 10, so 12 belongs to this sequence.


CROSSREFS

Cf. A006370, A006577.
Sequence in context: A208156 A135770 A091989 * A107835 A257966 A342814
Adjacent sequences: A078414 A078415 A078416 * A078418 A078419 A078420


KEYWORD

nonn


AUTHOR

Joseph L. Pe, Dec 29 2002


STATUS

approved



