Conway's Sequence
Level: Beginner 15–30 minConcepts: AlgorithmsStringsIncremental Design
Solutions: C# | TypeScript | Python
Generate terms of the look-and-say sequence (also known as Conway’s sequence). Each term is produced by describing the digits of the previous term.
How It Works
Start with "1". To get the next term, read the current term aloud:
"1"→ one 1 →"11""11"→ two 1s →"21""21"→ one 2, one 1 →"1211""1211"→ one 1, one 2, two 1s →"111221""111221"→ three 1s, two 2s, one 1 →"312211"
Requirements
Write a function that given a starting string and a number of iterations, returns the resulting term.
lookAndSay("1", 1)→"11"lookAndSay("1", 2)→"21"lookAndSay("1", 5)→"312211"
Also support generating a single next term:
nextTerm("1")→"11"nextTerm("111221")→"312211"
Test Cases
| Input | Iterations | Result |
|---|---|---|
"1" | 0 | "1" |
"1" | 1 | "11" |
"1" | 2 | "21" |
"1" | 3 | "1211" |
"1" | 4 | "111221" |
"1" | 5 | "312211" |
"2" | 1 | "12" |
"2" | 2 | "1112" |
"22" | 1 | "22" |
"1211" | 1 | "111221" |
"3211" | 1 | "13112111" |
Edge cases:
- Zero iterations returns the input unchanged
- Single digit input
- Input with runs longer than 9 (e.g. ten 1s →
"101"— decide how to handle)
Bonus
- Start from different seeds (not just
"1") and observe how sequences evolve - Calculate the length of the nth term without generating it (lengths grow by roughly 30% each iteration — look up Conway’s constant λ ≈ 1.303577)
- Support multi-character “digits” (e.g. atoms in Conway’s cosmological theorem)
Hint
Start with nextTerm for a single-character input. Then handle two identical characters. Then mixed characters. The multi-iteration version is just applying nextTerm repeatedly — get the single step right first.
Reference Walkthrough
Reference implementations in C#, TypeScript, and Python live at tddbuddy-reference-katas/conways-sequence. This is an F1 kata — 14 shared scenarios covering nextTerm single-step transforms (including the ten-ones double-digit-run-length edge case, described as "101") and lookAndSay(seed, n) with n = 0 returning the seed and negative n rejected.
- C# (.NET 8, xUnit, FluentAssertions 6.12.0) — walkthrough
- TypeScript (Node 20, Vitest 1.6, TS 5 strict) — walkthrough
- Python (3.11, pytest) — walkthrough
This kata ships in Agent Full-Bake mode at high gear: a single left-to-right run-counting pass, lands as one commit per language, with a brief walkthrough noting there are no builders because the algorithm’s inputs and outputs are the domain — no aggregates to construct, no value types to introduce, no collaborators to inject. The "3211" example from the Test Cases table above ("13112111") is mathematically inconsistent with the look-and-say rule; the reference scenarios use "131221" (one 3, one 2, two 1s). See the repo’s Gears section for when high gear is the right call.