Syracuse Function Calculator
Exact acceleratedoddCollatz/Syracuse(3n+1)/2^v2, not unaccelerated Collatz single-stepor global termination. Explicit bounded resource/branch and actual observations or independently verified parameters; no unproved infinite assertion certified.
Description
The accelerated odd Syracuse step removes every factor of two from 3n+1 after an odd input.
The accelerated odd Syracuse step removes every factor of two from 3n+1 after an odd input.1
This tool calculates that single step exactly from a canonical decimal string without claiming termination of an orbit.
When to use Syracuse Function Calculator
This tool calculates that single step exactly from a canonical decimal string without claiming termination of an orbit.
How to use Syracuse Function Calculator and how it works
- Prepare positive odd decimal, using the input definitions and matching units below.
- Enter the required fields and run Syracuse Function Calculator.
- Read result.exactNextOddSyracuseDecimal using the units, signs and ordering explained below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| actualPositiveOddDecimal | Canonical positive odd integer string of at most 128 digits. | string | Required; other constraints below |
Require a canonical decimal integer string of at most 128 digits, with no sign, whitespace or leading zeros except zero itself. Reject zero and even values. Use BigInt for 3n+1, repeatedly divide by two until odd and return the exact next odd value as a decimal string. Only one accelerated step is performed; no whole-orbit termination is asserted.
nextOdd=(3*n+1)/2^v2(3*n+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.exactNextOddSyracuseDecimal | Exact accelerated next odd integer as a decimal string. | string |
{
"input": {
"actualPositiveOddDecimal": "7"
},
"output": {
"result": {
"exactNextOddSyracuseDecimal": "11"
}
}
}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 Schnirelmann Basis Calculator for a complementary operation: A finite h-fold sumset records sums of exactly h elements, allowing repetition from a supplied basis.
Use Infinite Product Cosine Approximation for a complementary operation: A repeated half-angle cosine product has a sinc limit, but a finite depth remains a finite product.
References
-
Syracuse Function Calculator — tool.io
Similar or alternative tools
- Schnirelmann Basis Calculator
A finite h-fold sumset records sums of exactly h elements, allowing repetition from a supplied basis.
- Infinite Product Cosine Approximation
A repeated half-angle cosine product has a sinc limit, but a finite depth remains a finite product.