Description
Report adjacent canonical Lucas-number parities using L0=2,L1=1 and the period-three parity recurrence; no value enumeration.
A sequence rule specifies an index origin, state order, and relation among terms. Advancing one step, mapping an index, and checking a local residual answer different questions. Supplied coefficients or periods define a model; they do not establish that observations follow it.
Report adjacent canonical Lucas-number parities using L0=2,L1=1 and the period-three parity recurrence; no value enumeration.
When to use this tool
Use Sequence: Lucas Pair Parity Label when you need this particular index map, recurrence step, count, or local algebraic term under supplied sequence conventions.
How to use the tool and how it works
- Enter index. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Return currentOdd when index%3 is nonzero and nextOdd when (index+1)%3 is nonzero, inside result. Require integer index zero through one billion.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| index | Zero-based index unless the mechanics explicitly state otherwise. | Required. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
{
"input": {
"index": 0
},
"output": {
"result": {
"currentOdd": false,
"nextOdd": true
}
}
}Limitations and assumptions
- This uses a fixed modulo-three parity model rather than evaluating sequence terms. No alternative initial values or generalized Lucas parameters are supplied or verified.
- Outputs are nested inside result. The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Choose exact integer arithmetic when the index or coefficient range requires it. A complete sequence analysis needs actual terms and a consistent index and state-order convention beyond one local step.
References
Similar or alternative tools
- Lucas Recurrence One State Update
Parse current, previous, p, and q as bounded exact decimal integers and return next=p*current-q*previous as decimal text.
- Run Boundary Alternation Parity
Count alternations in an explicitly supplied two-label run-length encoding, preserving empty-stream status.