# hailstone_sequence: Hailstone Sequencer In collatz: Functions Related to the Collatz/Syracuse/3n+1 Problem

 hailstone_sequence R Documentation

## Hailstone Sequencer

### Description

Calculates the values of a hailstone sequence, from an initial value.

### Usage

```hailstone_sequence(
initial_value,
P = 2,
a = 3,
b = 1,
max_total_stopping_time = 1000,
total_stopping_time = TRUE,
verbose = TRUE
)
```

### Arguments

 `initial_value` (numeric|bigz) The value to begin the hailstone sequence from. `P` (numeric|bigz): Modulus used to divide n, iff n is equivalent to (0 mod P). Default is 2. `a` (numeric|bigz) Factor by which to multiply n. Default is 3. `b` (numeric|bigz) Value to add to the scaled value of n. Default is 1. `max_total_stopping_time` (int) Maximum amount of times to iterate the function, if 1 is not reached. Default is 1000. `total_stopping_time` (bool) Whether or not to execute until the "total" stopping time (number of iterations to obtain 1) rather than the regular stopping time (number of iterations to reach a value less than the initial value). Default is TRUE. `verbose` (bool) If set to verbose, the hailstone sequence will include control string sequences to provide information about how the sequence terminated, whether by reaching a stopping time or entering a cycle. Default is TRUE.

### Details

Returns a list of successive values obtained by iterating a Collatz-esque function, until either 1 is reached, or the total amount of iterations exceeds max_total_stopping_time, unless total_stopping_time is FALSE, which will terminate the hailstone at the "stopping time" value, i.e. the first value less than the initial value. While the sequence has the capability to determine that it has encountered a cycle, the cycle from "1" wont be attempted or reported as part of a cycle, regardless of default or custom parameterisation, as "1" is considered a "total stop".

### Value

A keyed list consisting of a \$values list of numeric | bigz along with a \$terminalCondition and \$terminalStatus

### Examples

```# Compute a hailstone sequence, which defaults to the total stopping time;
hailstone_sequence(5)
# Or only compute down to the regular stopping time;
hailstone_sequence(5, total_stopping_time=FALSE)
# Remove verbose messaging;
hailstone_sequence(5, verbose=FALSE)
# It will also stop on finding a cycle;
hailstone_sequence(-56)
# And can be parameterised;
hailstone_sequence(3, -1, 3, 1)
# The hailstone sequence can run on `bigz`;
hailstone_sequence(27+as.bigz("576460752303423488"))
```

collatz documentation built on Sept. 5, 2022, 9:06 a.m.