nth Fibonacci Number
Return F(n) exactly as a decimal string with F(0)=0 and F(1)=1; the index is capped at 100,000 for bounded computation.
Description
Fibonacci numbers add the preceding two terms, starting from zero and one.
Fibonacci numbers add the preceding two terms, starting from zero and one. Exact values quickly grow beyond ordinary safe-integer precision.1
The tool returns value. The indexing and output conventions below determine how to read these values.
When to use nth Fibonacci Number
Use this for the following task: Return F(n) exactly as a decimal string with F(0)=0 and F(1)=1; the index is capped at 100,000 for bounded computation. Use the input and output conventions below to reproduce the intended mathematical quantity.
How to use nth Fibonacci Number and understand its results
- Choose the required indexes, integers or sequence entries. Preserve decimal-string encodings where the field table specifies strings.
- Enter n according to the field table, then run the tool.
- Read value. Preserve exact decimal strings and the stated indexing or coefficient order.
- Keep exact decimal strings for subsequent integer arithmetic; distinguish them from any explicitly approximate numeric result.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| n | Zero-indexed term (resource limit 100000) | integer; minimum 0; maximum 100000 | Required |
Advance a two-value BigInt state n times and return the first state value as decimal text.
F(0)=0; F(1)=1; F(n)=F(n−1)+F(n−2) The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| value | Fibonacci number | string (integer/arbitrary) |
{
"input": {
"n": 50
},
"output": {
"value": "12586269025"
}
}Limitations and assumptions
The zero-based index is at most 100000. The tool returns one exact term, not a floating closed-form approximation or a full sequence.
Use the declared integer bounds and string formats. Large exact outputs remain decimal strings; numerical approximations use ordinary floating-point arithmetic. A rejected input is different from a valid zero count or false membership flag.
Alternative or Complementary methods
Choose nth Lucas Number when you need its operation: Return L(n) exactly as a decimal string with L(0)=2 and L(1)=1; the index is capped at 100,000 for bounded computation. Choose nth Tribonacci Number for the complementary operation: Return T(n) exactly with T(0)=T(1)=0, T(2)=1, and each later term the sum of the preceding three; the index is capped at 10,000.
Background reference: OEIS A000045.
References
-
OEIS A000045 — OEIS Foundation
Similar or alternative tools
- nth Lucas Number
Return L(n) exactly as a decimal string with L(0)=2 and L(1)=1; the index is capped at 100,000 for bounded computation.
- nth Tribonacci Number
Return T(n) exactly with T(0)=T(1)=0, T(2)=1, and each later term the sum of the preceding three; the index is capped at 10,000.