Pea pattern
Encyclopedia
A pea pattern is a mathematical
pattern
that, when following certain steps, will yield a string of patterned number
s.
The first Pea pattern made goes as such:
A number
is first named, such as 1, and the next number is derived by how many of each digit
is named in the number. There is one digit in 1, and there are 1 of that number, so the next number is 11. There are two 1's in 11, thus the next number in the series is 21. There is 1 2 and 1 1 in 21, so the number after that is 1211.
The original version of the Pea pattern had the digits listed in 'first-up' sequence thus the series for Pea(1) was as follows
1
11
21
1211
3112
132112
311322
232122
421311
14123113
41141223
24312213
32142311
23223114
32232114
23322114
32232114 these last two form a loop.
This is not the Look-and-Say series which proceeds 1, 11, 21, 1211, 111211.
As originally written the Pea pattern displays how many of each digit occurs in the series. There is an alternative Pea pattern which has the digits in ascending order. Pea(1)A [digits in ascending order] should be 1, 11, 21, 1112, 3112, 211213, 312213, 212223, 114213 etc and it becomes more interesting because Pea(0), Pea(1), Pea(2) & Pea(3) all loop after the 13th or 14th step.
As with the Look-and-say series, beginning with 22 yields an immediate loop. However Pea(33)A proceeds 333, 33, 23, 1213, 211213, etc
----
The second pea pattern is somewhat unique in that it goes backwards, beginning with a large number and going back down to a one-digit number. One could begin with a number such as 54739120829. The adjacent numbers are subtracted
from one another using absolute value, as such:
54739120829
1346812867
212271621
11056541
0151113
144002
30402
3442
102
12
1
Using this method the numbers will usually retract to 1 or 0.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
pattern
Pattern
A pattern, from the French patron, is a type of theme of recurring events or objects, sometimes referred to as elements of a set of objects.These elements repeat in a predictable manner...
that, when following certain steps, will yield a string of patterned number
Number
A number is a mathematical object used to count and measure. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers....
s.
The first Pea pattern made goes as such:
A number
Number
A number is a mathematical object used to count and measure. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers....
is first named, such as 1, and the next number is derived by how many of each digit
Digit
Digit may refer to:* Digit , one of several most distal parts of a limb—fingers, thumbs, and toes on hands and feet* Numerical digit, as used in mathematics or computer science* Hexadecimal, representing a four-bit number...
is named in the number. There is one digit in 1, and there are 1 of that number, so the next number is 11. There are two 1's in 11, thus the next number in the series is 21. There is 1 2 and 1 1 in 21, so the number after that is 1211.
The original version of the Pea pattern had the digits listed in 'first-up' sequence thus the series for Pea(1) was as follows
1
11
21
1211
3112
132112
311322
232122
421311
14123113
41141223
24312213
32142311
23223114
32232114
23322114
32232114 these last two form a loop.
This is not the Look-and-Say series which proceeds 1, 11, 21, 1211, 111211.
As originally written the Pea pattern displays how many of each digit occurs in the series. There is an alternative Pea pattern which has the digits in ascending order. Pea(1)A [digits in ascending order] should be 1, 11, 21, 1112, 3112, 211213, 312213, 212223, 114213 etc and it becomes more interesting because Pea(0), Pea(1), Pea(2) & Pea(3) all loop after the 13th or 14th step.
As with the Look-and-say series, beginning with 22 yields an immediate loop. However Pea(33)A proceeds 333, 33, 23, 1213, 211213, etc
----
The second pea pattern is somewhat unique in that it goes backwards, beginning with a large number and going back down to a one-digit number. One could begin with a number such as 54739120829. The adjacent numbers are subtracted
Subtraction
In arithmetic, subtraction is one of the four basic binary operations; it is the inverse of addition, meaning that if we start with any number and add any number and then subtract the same number we added, we return to the number we started with...
from one another using absolute value, as such:
54739120829
1346812867
212271621
11056541
0151113
144002
30402
3442
102
12
1
Using this method the numbers will usually retract to 1 or 0.