Moser-de Bruijn Numbers Generator

Write a number in base 4 and forbid the digits 2 and 3: you get 0, 1, 4, 5, 16, 17, 20, 21, 64, 65, 68, 69, 80... — the Moser-de Bruijn numbers, the sums of distinct powers of 4. The sequence is 2-automatic, part of the Stanley family, and carries one of the prettiest structural laws in additive number theory: every integer splits uniquely as a plus twice b with both parts in the set.

Moser-de Bruijn Numbers Generator builds the sequence term by term by translating binary into base 4 — term m is the bits of m read as quaternary digits. Choose a start index and a count, inspect the base-4 form on every row, and copy or download the complete list. BigInt values stay exact at any size.

• Exact construction: Term m = binary(m) read as base-4 digits — an O(log m) BigInt translation.
• Start anywhere: Continue from any index, up to a million, with up to 10,000 consecutive terms.
• Base-4 on every row: The digit string 0/1 that defines the set is rendered for each term.
• BigInt exactness: No floating point anywhere; hundreds of digits stay exact.
• Copy or download: One click exports the whole run as index = value lines.
• Reference tab: The splitting law, the Stanley identity, the 2-automaton and the powers-of-4 view.
• Free and private: Everything runs locally — nothing is uploaded, stored or logged.

1. Set the start index — which term m to begin with (0 to 1,000,000).
2. Set the count — how many consecutive terms to generate (1 to 10,000).
3. Generate — rows appear with index, value and base-4 digits.
4. Watch the structure — every base-4 form is a string of only 0s and 1s.
5. Copy or download — the complete run for analysis or reuse.

Example 1 — The opening. Start 0, count 8: 0, 1, 4, 5, 16, 17, 20, 21. Their base-4 forms — 0, 1, 10, 11, 100, 101, 110, 111 — mirror the binary counting of the indexes.

Example 2 — The doubling pattern. Generate 16 terms and observe the blocks: the first eight terms are exactly half of the second eight, which share the base-4 leading digit 1.

Example 3 — The splitting law in action. Pick 17 in the list: 17 = 1 + 2 x 8 — and 1 and 8 are both members of the sequence, exactly as the splitting theorem promises.

Example 4 — Big terms. Start 5000, count 6: the values jump past 10^24 with base-4 forms that are pure 0/1 strings of 40+ digits.

Example 5 — Cross-check with Stanley. Run the Stanley generator with count 12 and compare: the lists are identical, proving the greedy 3-term-free rule produces the same set.

• Instant generation: Any run of the sequence in one click, no manual base conversion.
• Definition visible: The base-4 0/1 structure on every row teaches the property by inspection.
• Arbitrary scale: BigInt translation means the numbers keep growing with zero loss of precision.
• Text-ready output: Index = value lines paste directly into spreadsheets or papers.
• Structural insight: The reference tab connects the set to Stanley sequences and additive number theory.
• Private by design: Nothing leaves the browser; no uploads, no logs.