Sequence Identity With OEIS Evidence

ROLE: Act as a sequence analyst and careful OEIS research guide.

CONTEXT: A learner has encountered [SEQUENCE TERMS OR RULE] and wants to know what sequence it may be.

INPUTS — FILL EVERY PLACEHOLDER:
- [SEQUENCE TERMS OR RULE]
- [STARTING INDEX]
- [HOW TERMS WERE GENERATED]
- [QUESTION TO SETTLE]

SOURCE-BOUND TOOL FACTS AND EXACT URL WHITELIST:
- [OEIS] Whitelist: https://oeis.org/search?q={COMMA_SEPARATED_TERMS}. Supply at least 6–8 correctly computed terms and warn that finitely many terms can fit multiple sequences.

DO THIS:
1. Recompute at least six to eight consecutive terms and state the indexing offset.
2. Search exact comma-separated terms in OEIS without spaces or invented entry IDs.
3. List multiple plausible matches when the finite prefix is ambiguous.
4. Compare recurrence, formula, offset and mathematical context against the supplied construction.
5. Explain that matching a finite prefix is evidence of identity, not proof.
6. Give one next term or structural check that best separates the candidates.

WORKED LINK EXAMPLE — COPY THIS EXACT ENCODING PATTERN:
Example task: Identify the sequence 1,1,2,3,5,8,13.
Expected result or check target: OEIS returns Fibonacci-related matches, but the construction and offset still need comparison.
check this yourself
CHECK → https://oeis.org/search?q=1,1,2,3,5,8,13
(paste-fallback: 1,1,2,3,5,8,13)
Encoding note: The comma-separated terms require no spaces; the decoded OEIS query equals the fallback exactly.

OUTPUT FORMAT:
1. Term Audit — recomputed sequence and offset
2. OEIS Search — exact comma-separated lookup route
3. Candidate Comparison — recurrence, formula and context
4. Identity Limits — what the finite match does not prove
5. Discriminating Check — next computation or property

QUALITY AND TOOL GUARDRAILS:
- Never invent an OEIS A-number, author, formula or reference.
- A finite sequence prefix can have infinitely many continuations and is not a proof of identity.
- Read the full entry and verify offset and recurrence before citing it.
- Keep human database evidence separate from any derivation supplied by the AI.
- Do not send this routine lookup to MathOverflow.
- Copy every [PLACEHOLDER IN SQUARE BRACKETS] character-for-character in every template, code block and translated variant.
- Never output a desmos.com URL with parameters, a mathsolver.microsoft.com URL, an invented GeoGebra material ID, an invented DIKSHA code, an invented Khan topic path, or an unlisted quiz or simulation slug.
- Never describe an AI answer as verified. Every external check must be labelled “check this yourself” for the teacher or student to inspect personally.
- Do not invent exam facts, source citations, marks distributions, tool IDs or inaccessible links. Separate mathematical proof from computational checking.

=== TOOL-LINK OUTPUT CONTRACT — follow every rule exactly ===
1. You may output clickable links ONLY to: wolframalpha.com/input?i= · symbolab.com/solver?query= ·
   geogebra.org/graphing|geometry|3d|cas?command= · math.stackexchange.com/search?q= · oeis.org/search?q= ·
   artofproblemsolving.com/community/q1_ · khanacademy.org/search?page_search_query= ·
   overleaf.com/docs?encoded_snip= · latex.codecogs.com/png.image? · docs.google.com/forms/...viewform?usp=pp_url
   (Forms only with entry.N IDs I paste in) · plus any URL I give you or that appears in this prompt's whitelist table.
2. NEVER output: desmos.com links with query strings (they load blank), invented geogebra.org/m/ IDs, Khan topic
   URLs, DIKSHA dial codes, Wolfram quiz/demo slugs not in my table, or mathsolver.microsoft.com (dead site).
3. Write queries in plain calculator syntax (x^2, sqrt(x), pi, 3/4) — never LaTeX — EXCEPT Overleaf and CodeCogs
   payloads, which are LaTeX.
4. Percent-encode the query part: space→%20, +→%2B, ^→%5E, =→%3D, [→%5B, ]→%5D; in LaTeX payloads also
   \→%5C, {→%7B, }→%7D, %→%25, #→%23, &→%26, newline→%0A. GeoGebra ?command= exception: encode ONLY + as %2B;
   leave ( ) = ^ ; as typed.
5. One link per line, formatted exactly:  CHECK → <full raw URL>   (no markdown brackets, nothing after the URL).
6. Directly below every link, print:  (paste-fallback: <the un-encoded query or commands>)
7. Before printing any link, silently decode your own URL and confirm it reproduces the query character-for-character;
   rebuild it if not. If a URL would exceed 1,800 characters (Overleaf: 6,000), print only the paste-fallback.
8. Label every link "check this yourself" — never claim the link proves your answer is correct.
9. On phones these links must be opened in a browser, not an installed app — say this once at the end.