Recreational Mathematics
Semi-Selfie Digit-Partition
Perfect Power Generator
Search note: Long numbers and wide ranges can require many partition and sign checks. The generator stops at the selected result limit, and the Stop button can end a long search safely.
Digit blocks are consecutive and remain in their original order. The first block is kept positive; its globally sign-reversed counterpart would only duplicate an even-power result.
What is tested?
Every cut between adjacent digits is considered. For 2401, possible partitions include 2|4|0|1, 24|0|1, 2|40|1, 240|1, and others. Each permitted sign pattern is then tested exactly with integer arithmetic.
What counts as a result?
A representation is reported only when the signed block sum has absolute value greater than one and raising it to an integer exponent reconstructs the original number exactly. Different partitions, signs, bases, and exponents are retained.