Look-and-Say Sequence

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Each term describes the previous term by counting runs of identical digits.

Starting from a single digit, each term is obtained by reading the previous term aloud and counting consecutive identical digits. Starting from 1: one 1 → 11; two 1s → 21; one 2, one 1 → 1211; one 1, one 2, two 1s → 111221; and so on. The sequence is 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211. Conway showed that the length of terms grows by a fixed factor (Conway's constant ≈ 1.303577).

a_{n+1} = "read" a_n as runs of identical digits

• 1 → 11 (one 1)
• 11 → 21 (two 1s)
• 21 → 1211 (one 2, one 1)
• 1211 → 111221 (one 1, one 2, two 1s)

How to recognize it

• The only digits that appear are 1, 2, and 3 (proven by Conway)
• Each term reads as a description of the previous term
• Term lengths grow but not by a simple integer ratio

Common mistakes

• Reading digits individually without grouping identical runs
• Starting from 2 or 3 — the classic sequence starts from 1
• Swapping the order of (count, digit) pairs

Practice guidance

Number Sequences