Baum-Sweet Numbers Generator

Scan the binary digits of n and strike out every block of consecutive zeros of odd length: the survivors are exactly the n with b(n) = 1. That one rule produces the Baum-Sweet sequence — 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, ... — one of the first "automatic" sequences ever studied, still famous for the almost-mysterious smoothness its generating function displays near the unit circle.

Baum-Sweet Numbers Generator evaluates b(n) by the run rule itself for any start index, prints each binary form together with its zero-run analysis, and keeps a live census of 1s across the block.

• Run-rule faithful: Odd-length zero blocks detected exactly, including trailing zeros.
• Binary evidence on every row: The runs being judged are displayed next to each value.
• Live census: The count of b(n) = 1 across the window updates as you scan.
• Start anywhere: Any index from 0 to 1,000,000, up to 10,000 consecutive terms.
• Reference tab: The automaton, the Baum-Sweet theorem, OEIS data and history.
• Free and private: All computation is local; nothing is uploaded, stored or logged.

1. Set the start index — first n to evaluate (0 to 1,000,000).
2. Set the count — consecutive values to generate (1 to 10,000).
3. Generate — binary forms appear with their runs of zeros annotated.
4. Read the census — the share of 1s changes block by block.
5. Copy or download — the run as index = value lines.

Example 1 — Small values. Count 16: 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1. Position 4 is 1 because 100 keeps an even trailing zero block.

Example 2 — A single odd zero. n = 5 (101) holds a lone zero — odd length — so b(5) = 0.

Example 3 — Even blocks survive. n = 12 (1100) ends in two zeros, an even block, giving b(12) = 1.

Example 4 — Long zero runs. n = 8 (1000) has a block of three zeros: odd, so b(8) = 0, while its neighbor n = 16 (10000) parades four zeros and scores 1.

Example 5 — Large indices. Start 250,000, count 12: twenty-digit binary forms, each judged by its longest trailing zero run.

• Definition-faithful: The run rule decides every value; nothing else enters.
• Evidence on screen: Binary and zero-run annotations explain each decision.
• Flexible ranges: Start anywhere and examine any window up to 10,000 terms.
• Insightful stats: The census line illuminates density behavior of the 1s.
• Clean output: Copy or download index = value lines ready for analysis.
• Private by design: No server, no upload, no logging.