Collatz Max Value Calculator
ExactintegerCollatzpeakonlywhen1reached with inexplicit budget, start canonical decimal≤ 128 digits, no global termination proof. Explicit bounded resource/branch and actual observations or independently verified parameters; no unproved infinite assertion certified.
Description
An observed Collatz maximum is meaningful only for the orbit segment actually followed under a stated stopping condition.
An observed Collatz maximum is meaningful only for the orbit segment actually followed under a stated stopping condition.1
This tool returns an exact maximum when one is reached within a finite budget, without asserting universal termination.
When to use Collatz Max Value Calculator
Use this tool to obtain an exact maximum when one is reached within a finite budget, without asserting universal termination.
How to use Collatz Max Value Calculator and how it works
- Prepare actualPositiveStartDecimal, actualIterationBudget, with the units, conventions and assumptions below.
- Enter the required fields and run Collatz Max Value Calculator.
- Read result.observedMaximumUntilOneDecimal using the output definitions below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| actualPositiveStartDecimal | Canonical positive decimal integer string without leading zeros, at most 128 digits. | string | Required; other constraints below |
| actualIterationBudget | Positive integer maximum step count, at most 100000. | number | Required; finite; other constraints below |
Require a canonical positive decimal integer string of at most 128 digits and an integer iteration budget from 1 to 100,000. Track BigInt values under n/2 for even n and 3*n+1 for odd n, retaining the largest encountered value including the starting value. Return its exact decimal string once 1 is reached within the budget; exhaustion is an input/run error rather than a returned partial peak. A starting value of 1 succeeds without a step.
n_next=(n even ? n/2 : 3*n+1); maximum=max(all values through first 1) Apply the input ordering, units and branch conditions stated above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the calculated or selected fields below. | object |
| result.observedMaximumUntilOneDecimal | Largest exact Collatz value through first 1, as a decimal integer string. | string |
{
"input": {
"actualPositiveStartDecimal": "27",
"actualIterationBudget": 1000
},
"output": {
"result": {
"observedMaximumUntilOneDecimal": "9232"
}
}
}Limitations and assumptions
The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.
All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.
Alternative or Complementary methods
Use Deficiency Ratio Calculator for a complementary operation: A deficiency ratio compares an integer with the sum of its proper divisors.
Use Amicable Pair Sum Calculator for a complementary operation: An amicable pair requires each integer's proper-divisor sum to equal the other integer.
References
-
Collatz Max Value Calculator — tool.io
Similar or alternative tools
- Deficiency Ratio Calculator
A deficiency ratio compares an integer with the sum of its proper divisors.
- Amicable Pair Sum Calculator
An amicable pair requires each integer's proper-divisor sum to equal the other integer.