Stanley Numbers Generator

Take one greedy rule — never choose a number that completes a 3-term arithmetic progression with two numbers already chosen — and apply it forever, starting from 0 and 1. The result is the most touching sequence in additive combinatorics: 0, 1, 3, 4, 9, 10, 12, 13, 27, 28, 30, 31... — the numbers with only digits 0 and 1 in base 3, otherwise known as the Stanley sequence S(0, 1).

Stanley Numbers Generator runs the greedy construction itself: each candidate faces the midpoint test (a + b = 2c) and the endpoint test (c = 2a − b) against the growing set before admission. Choose a start index and count; each row shows the value and its base-3 digits, making the closure theorem visible term by term.

• True greedy construction: Every term admitted only after the 3-term arithmetic-progression test passes.
• Base-3 on every row: The 0/1 digit rendering demonstrates the ternary closure theorem as terms appear.
• Start anywhere: From index 0 to a million, up to 10,000 consecutive terms.
• BigInt exactness: Hundreds of digits with zero rounding.
• Copy or download: One click export of the full run as index = value lines.
• Reference tab: The greedy proof, S(0, 1, 4) = S(0, 1) note, Odlyzko–Stanley remarks.
• Free and private: All selection runs locally — nothing is uploaded, stored or logged.

1. Set the start index — which term to begin with (0 to 1,000,000).
2. Set the count — consecutive terms to generate (1 to 10,000).
3. Generate — the greedy rule runs against the chosen set and admits or rejects candidates.
4. Inspect the base-3 digits — every value uses only 0 and 1.
5. Copy or download — the complete run for analysis.

Example 1 — The greedy start. Count 10: 0, 1, 3, 4, 9, 10, 12, 13, 27, 28. Notice 2 is skipped because 0, 1, 2 form a progression with earlier members.

Example 2 — Midpoint and endpoint tests. Candidate 2 completes (0, 1, 2) as an end; candidate 5 is rejected because 3 = (1 + 5)/2 is already chosen, making (1, 3, 5). Each candidate faces both tests against the whole set.

Example 3 — Base-3 view. Generate 12 terms: the ternary forms read 0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011 — binary counting wearing base-3 clothing.

Example 4 — The closure check. Generate 16 terms and read the base-3 column: no digit 2 ever appears — the members are exactly the numbers whose ternary form uses only 0 and 1.

Example 5 — Large terms. Start 1000, count 5 — the values reach past a million with base-3 forms of 10+ digits, computed exactly by BigInt.

• Definition-faithful: The actual greedy rule runs; nothing is replaced by a shortcut.
• Theorem on screen: The ternary digit-set closure is demonstrated term by term.
• Flexible ranges: Start anywhere and take any run length up to 10,000.
• Exact at scale: BigInt keeps greedy checks and values precise forever.
• Structured output: Values plus base-3 digits export cleanly for further work.
• Private by design: The greedy loop stays in the browser; nothing is uploaded or logged.