Definition:Pea Pattern

Definition

A pea pattern is a generic term use for any one of a number of similar sequences.

The first term $p_0$ is an arbitrary integer.

$p_n$ is formed from $p_{n - 1}$ as follows.

First, the distinct digits in $p_{n - 1}$ are counted, and the number of each is noted.

The count of each distinct digit is concatenated with an instance of the digit itself.

Then those concatenations are themselves concatenated into $p_n$ according to a predetermined order.

Sequential Order

For the sequential pea pattern, the concatenation into $p_n$ is in sequential order of how the first instance of the distinct digits appear in $p_{n - 1}$.

Ascending Order

For the ascending pea pattern, the concatenation into $p_n$ is in ascending order of the distinct digits of $p_{n - 1}$.

Descending Order

For the descending pea pattern, the concatenation into $p_n$ is in descending order of the distinct digits of $p_{n - 1}$.

Also see

• Definition:Look-and-See Sequence
• Results about pea patterns can be found here.

Linguistic Note

The origin of the term pea pattern is unclear.

The terms ascending pea pattern, descending pea pattern and sequential pea pattern appear not to be standard, as many sources focus on one of the variants and ignore the others.