1 then 11 then 21 then 1211
- 1 then 11 then 21 then 1211
- String processing in python: look-and-say sequence
- Berlin now & then – episode 3: lichterfelde kaserne
- 1 11 21 1211 111221
- Finding the 100th term in a sequence | sequences, series and
- 5.14 avl tree insertion | with solved example | data structures
- Can you crack the code? solution!
- Look-and-say sequence
- Qual o próximo termo da sequência 1,11,21,1211,111221
String processing in python: look-and-say sequence
I frequently need to generate the look and tell series, so I made this easy online tool to help me out. It allows you to measure as many look and say series terms as you need from any starting state. It runs in the browser and is powered by futuristic alien technology.
From the “abc” initial value, we generate the look and say series in this example. We explain what we see by saying “one a, one b, one c” and writing “1a1b1c” on a piece of paper. Every subsequent value’s digits increase or decrease, but the three initial letters remain the same.
This is the only time the look and tell series is used where the words remain the same. We begin with the value “22” and define it as “two twos,” yielding the same next term “22.”
In this case, the sequence begins with a single letter “k.” We make 5 objects and use the arrow symbol to distinguish them. If you look closely, you’ll notice that the digits only appear on the left hand, while “k” is always on the right! The same thing will happen with each and every letter symbol (including digits). This sequence is known as the Conway sequence if k=3.
Berlin now & then – episode 3: lichterfelde kaserne
In two previous posts, I looked at Conway’s famous “look-and-say” sequence 1, 11, 21, 1211, 111221, 312211, and a simple binary version of the sequence, which was obtained by repeatedly describing the sequence’s previous name. In this article, I’ll use similar techniques to investigate two more variants of the sequence: one in which each word is read in ternary, and another in which no digit larger than 2 can be used to describe its meanings.
We’ll approach these sequences the same way we attack standard look-and-say sequences: by creating a “periodic table” of elementary non-interacting subsequences that all terms in the sequence are made up of. The rate of growth of the length of the terms in the sequences, as well as the limiting distribution of the different digits in the sequence, will then be determined using standard recurrence relation techniques.
We’ve already looked at the regular (decimal) look-and-say sequence, which is equivalent to the base-4 version of the sequence because it never contains a digit of 4 or larger, and the binary version of the sequence, so it’s only natural to wonder what happens in the intermediate case of the ternary (base-3) version of the sequence: 1, 11, 21, 1211, 111221, 1012211,… (see A001388).
1 11 21 1211 111221
The lines depict the development of digits in look-and-say sequences with starting points of 23 (red), 1 (blue), 13 (violet), and 312 (green) (green). When viewed on a logarithmic vertical scale, these lines appear to be straight lines with slopes equal to Conway’s constant.
The sequence continues to evolve indefinitely. Except for the degenerate sequence, any variant identified by starting with a different integer seed number will (eventually) grow indefinitely. 22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22 (In the OEIS, sequence A010861) [three]
Any sequence eventually splits (“decays”) into a sequence of “atomic elements,” which are finite subsequences that never interact with their neighbors, according to Conway’s cosmological theorem. There are 92 elements that only have the digits 1, 2, and 3, which John Conway named after chemical elements up to uranium and dubbed the sequence audioactive. For each digit other than 1, 2, and 3, there are two “transuranic” components. [three]  where = 1.303577269034… (OEIS sequence A014715) is a 71-degree algebraic number. [three] Conway established this truth, and the constant is known as Conway’s constant. Any variant of the sequence beginning with a seed other than 22 yields the same result.
Finding the 100th term in a sequence | sequences, series and
This is referred to as a “look and tell” series.
5.14 avl tree insertion | with solved example | data structures
the first term
Can you crack the code? solution!
What do you think about #1?
Qual o próximo termo da sequência 1,11,21,1211,111221
What do you think you’re seeing? two (1) becomes twenty-third twenty-first twenty-first twenty-first twenty-first twenty-first What do you think you’re seeing? one (2) and one (1), resulting in 12114th-1211th. What do you think you’re seeing? 1112215th-111221sixth-312211seventh-13112221eighth-1113213211ninth-31131211131221tenth-13211311123113112211 Your most recent term was #10. Here are the next five11-1113122113311213211321222112-311311222123211211131221131211321113-13211321321131211321113-13211321321131211321113-13211321321131211321113-13211321321131211321113-13211321321131211321113-11131221131211131221131211321113-11131221131211131221131211321113-1113122113121113122113121321123