A306378 Number of steps of applying "Erase or triple" protocol to n before reaching 0, 5, 7, or 89.

0, 16, 10, 15, 10, 0, 9, 0, 9, 14, 22, 1, 9, 3, 24, 8, 19, 8, 8, 3, 10, 11, 1, 6, 8, 3, 22, 13, 3, 16, 21, 8, 13, 1, 19, 21, 8, 2, 12, 2, 12, 4, 23, 13, 1, 7, 19, 12, 18, 19, 12, 7, 26, 13, 7, 1, 30, 2, 3, 18, 9, 18, 12, 10, 15, 12, 1, 32, 14, 5, 6, 21, 7, 21

Offset

0,2

Comments

The "Erase or triple" protocol is described in A300148 and each trajectory converges to one of 4 loops. Since for n > 9876543210, this protocol take n to a number <= 876543210, it suffices to only look at the trajectories of n under this protocal for 0 <= n <= 9876543210.

a(n) <= 52 for all n. For n <= 9876543210, a(n) is maximal at a(n) = 52 for 994 different numbers, the smallest of which is 445016392 and the largest of which is 9849720163 and all these trajectories converge to 0. Each of these 994 numbers either has nonunique digits or is pandigital, and thus cannot be the result of an "erase" operation, i.e. cannot be part of trajectory that started larger than 9876543210, thus for n > 9876543210, a(n) <= 51 + 1 = 52.

Links

Table of n, a(n) for n=0..73.

Example

The trajectory of 2 is 2, 6, 18, 54, 162, 486, 1458, 4374, 37, 111, 0, 0, ...
The trajectory of 10 is 10, 30, 90, 270, 810, 2430, 7290, 21870, 65610, 510, 1530, 4590, 13770, 130, 390, 1170, 70, 210, 630, 1890, 5670, 17010, 7, ...

Crossrefs

Cf. A300148, A300149, A300150, A300151.

Sequence in context: A303317 A154615 A040242 * A232999 A217157 A070578

Adjacent sequences: A306375 A306376 A306377 * A306379 A306380 A306381

Keyword

nonn

Author

Chai Wah Wu, Feb 11 2019

Status

approved