Glossary
To find the next integer in a 1chain, multiply by 4 and add 1.
A positive integer less than 2k, used when defining pivot formats.
An nchain. Used when not referring to a specific nchain.
Integers converge if they step down to the same integer.
An even integer.
The step down function.
An infinite set of levels.
A positive integer which may be odd or even.
A power of 2.
The symbol for a level. If followed by a variable it refers to a relative level, e.g . Lr is the level below L(r+1). If followed by a numeric value it refers to an actual level in the 3x+1 tree, e.g. integers at L6 step down to 1 in six steps.
Integers that converge after the same number of steps down are at the same level.
An integer in an nchain subsequent to the pivot. Links are defined as a function of the previous integer in the nchain by a repeated cycle of functions.
A thread is in a loop if it constantly repeats a cycle of integers.
A positive integer.
A sequence of integers at the same level that converge to the same integer at a lower level after n steps and that do not converge until reaching that integer. An nchain consists of a pivot followed by an infinite number of links.
An odd integer.
The previous integer in an nchain, used in the functions defining an nchain.
The first integer in an nchain.
A sequence of integers obtained by stepping up (not necessarily the reverse of a thread).
Given x, calculate 3x+1 and then divide by 2 until an odd integer is obtained.
Perform a step.
Find an integer at the next higher level which steps down to a given integer or to an integer at the same level as the given integer.
A sequence of odd integers obtained by stepping down.