Editing Look-and-say sequence (section)

==Variations==
{{Unreferenced section|date=May 2022}}
There are many possible variations on the rule used to generate the look-and-say sequence. For example, to form the "pea pattern" one reads the previous term and counts all instances of each digit, listed in order of their first appearance, not just those occurring in a consecutive block.<ref name="pea pattern study">{{cite arXiv |last1=Kowacs |first1=André |title=Studies on the Pea Pattern Sequence |date=2017 |class=math.HO |eprint=1708.06452 }}</ref><ref>{{cite journal |last1=Dassow |first1=J. |last2=Marcus |first2=S. |last3=Paun |first3=G. |title=Iterative reading of numbers and "black-holes" |journal=Periodica Mathematica Hungarica |date=1 October 1993 |volume=27 |issue=2 |pages=137–152 |doi=10.1007/BF01876638}}</ref>{{verify source|date=April 2025}} So beginning with the seed 1, the pea pattern proceeds 1, 11 ("one 1"), 21 ("two 1s"), 1211 ("one 2 and one 1"), 3112 ("three 1s and one 2"), 132112 ("one 3, two 1s and one 2"), 311322 ("three 1s, one 3 and two 2s"), etc. This version of the pea pattern eventually forms a cycle with the two "atomic" terms 23322114 and 32232114. Since the sequence is infinite, the length of each element in the sequence is bounded, and there are only finitely many words that are at most a predetermined length, it must eventually repeat, and as a consequence, pea pattern sequences are always eventually [[periodic sequence|periodic]].<ref name="pea pattern study" />

Other versions of the pea pattern are also possible; for example, instead of reading the digits as they first appear, one could read them in ascending order instead {{OEIS|id=A005151}}. In this case, the term following 21 would be 1112 ("one 1, one 2") and the term following 3112 would be 211213 ("two 1s, one 2 and one 3"). This variation ultimately ends up repeating the number 21322314 ("two 1s, three 2s, two 3s and one 4").

These sequences differ in several notable ways from the look-and-say sequence. Notably, unlike the Conway sequences, a given term of the pea pattern does not uniquely define the preceding term. Moreover, for any seed the pea pattern produces terms of bounded length: This bound will not typically exceed {{nobr| 2 × ''[[Radix]]'' + 2  digits}} (22&nbsp;digits for [[decimal]]: {{nobr|radix {{=}} 10}}) and may only exceed {{nobr| 3 × ''[[Radix]]''  digits}} (30&nbsp;digits for decimal radix) in length for long, degenerate, initial seeds (sequence of "100 ones", etc.). For these extreme cases, individual elements of decimal sequences immediately settle into a [[permutation]] of the form {{nobr|{{math| ''a''0 ''b''1 ''c''2 ''d''3 ''e''4 ''f''5 ''g''6 ''h''7 ''i''8 ''j''9 }} }} where here the letters {{math| ''a''–''j'' }} are placeholders for digit counts from the preceding sequence element.