A087252 Numbers that are divisible by 4, but cannot be the largest peak value in a 3x+1 trajectory, regardless of the initial value.

12, 28, 36, 44, 60, 76, 92, 108, 120, 124, 140, 156, 164, 172, 188, 204, 216, 220, 236, 248, 252, 268, 284, 292, 300, 316, 328, 332, 348, 364, 376, 380, 388, 396, 412, 420, 428, 432, 436, 440, 444, 460, 476, 484, 492, 496, 500, 504, 508, 516, 524, 540, 548

Offset

1,1

Links

Table of n, a(n) for n=1..53.

Example

It is provable that (beyond 1 and 2) the largest peak value in any 3x+1 (Collatz) trajectory must be a multiple of 4. However, an infinite number of multiples of 4 exist that cannot be the largest peak value of such a trajectory. E.g., no integer of the form 16k+12 = 4*(4k+3) (where k is a nonnegative integer) can be a largest peak value, because the trajectory immediately after the value 16k+12 would consist of the values 8k+6, 4k+3, 12k+10, 6k+5, and 18k+16, which exceeds 16k+12.

Crossrefs

Cf. A025586.

Sequence in context: A196475 A253534 A255136 * A141274 A224613 A134618

Adjacent sequences: A087249 A087250 A087251 * A087253 A087254 A087255

Keyword

nonn

Author

Labos Elemer, Sep 08 2003

Extensions

Definition and example reworded by Jon E. Schoenfield, Sep 01 2013

Status

approved