Gijswijt Numbers Generator

Take every prefix of a sequence, ask it how many times it ends with a repeated block, and glue that answer on as the next term. Repeat forever, starting from 1, 1. The result — found by Dion Gijswijt in 1991 — is one of the slowest-growing sequences in mathematics: 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 2, 3, ... Terms are always 1, 2, 3 or 4, yet the first 4 takes 220 steps to arrive.

Gijswijt Numbers Generator runs the curling-number process exactly: each step scans the current prefix for the largest repeated tail block and appends the answer. Start anywhere, generate thousands of terms, watch the block-decoration structure and the records (1, 2, 3, 4) accumulate in real time.

• True definition-process: Every term is the curling number of its prefix, computed exactly.
• Record markers: First occurrences of 2, 3 and 4 are flagged so the slow growth is obvious.
• Start anywhere: Any origin up to position 1,000,000, with up to 10,000 consecutive terms.
• Fast prefix scan: A prefix-function scan over the reversed prefix detects maximal repeated tails in near-linear time.
• Reference tab: Curling-number definition, the no-5 proof sketch, first-occurrence table, and the conjecture.
• Free and private: All computation is local; nothing is uploaded, stored or logged.

1. Set the start index — which term to begin with (1 to 1,000,000).
2. Set the count — consecutive terms to generate (1 to 10,000).
3. Generate — the prefix is built from the beginning, and each curling number is appended exactly.
4. Watch the records — first occurrences of 2, of 3, and of 4 at 9 and 220.
5. Copy or download — the run as index = value lines.

Example 1 — The beginning. Generating 12 terms gives 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2. The prefix "112" ends with two copies of "2", so the third curling answer is 2.

Example 2 — A three-copy tail. Terms 6 to 8: "112112" ends "112112" = two copies of "112"; the next prefix ends in 2, 2, 2, three copies of "2" — so term 8 is 3.

Example 3 — The first 4. Generate from index 215 with count 12: the 4 sits right at position 220, after a carefully stacked tail of nested blocks.

Example 4 — Slow growth. Run 2,000 terms: values stay inside {1, 2, 3, 4}. The count of runs is far larger than the values — the hallmark of this sequence.

Example 5 — Self-similarity. Generate 500 terms and watch the block pattern "112112223" repeat at larger and larger scales — the same shape the proof of no-5 exploits.

• Definition-faithful: The true curling-number process runs; no approximation anywhere.
• Exact records: First occurrences of each value are computed, not cited.
• Fast at length: Near-linear steps reach tens of thousands of terms smoothly.
• Uncluttered output: One index = value per row, copyable and downloadable.
• Educational reference: Definitions, history and the open conjecture in one tab.
• Private by design: No uploads, no storage, no logging.