Dudeney number¶
A base-dependent natural number that is a perfect cube whose digit sum equals its cube root.
Core Idea¶
In the classical decimal case, m is a Dudeney number when m equals n cubed and the sum of the base-ten digits of m equals n; generalized versions vary the base and exponent. Exponentiation produces the digit string, digit summation maps it back to a candidate root, and solutions are fixed points of the resulting digit-power transform. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
Scope of Application¶
Dudeney number belongs to recreational number theory and is useful where the analyst can specify the typed recreational number theory carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the base and exponent are fixed, the number is the stated power of a natural root, and its digit sum in that base equals the root. The scope is broad within that domain but bounded by the need for the base and exponent are fixed, the number is the stated power of a natural root, and its digit sum in that base equals the root. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the base and exponent are fixed, the number is the stated power of a natural root, and its digit sum in that base equals the root the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Dudeney number can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Dudeney number. Dudeney number compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed recreational number theory carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the base and exponent are fixed, the number is the stated power of a natural root, and its digit sum in that base equals the root independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of recreational number theory because they reuse the typed recreational number theory carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Exponentiation produces the digit string, digit summation maps it back to a candidate root, and solutions are fixed points of the resulting digit-power transform., and type the carrier, state every parameter and convention in the definition, test that the base and exponent are fixed, the number is the stated power of a natural root, and its digit sum in that base equals the root, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Dudeney number Domain-specific
Parents (1) — more general patterns this builds on
-
Dudeney number is a kind of Fixed Point Prime
The proposed strict upward parent is
prime:fixed_point.
Hierarchy path (1) — routes to 1 parentless root
- Dudeney number → Fixed Point
Neighborhood in Abstraction Space¶
Dudeney number sits in a moderately populated region (42nd percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Digit Properties & Recreational Numbers (6 abstractions)
Nearest neighbors
- Keith number — 0.93
- Amenable number — 0.91
- Taxicab number — 0.90
- 15 puzzle — 0.89
- Persistence of a number — 0.89
Computed from structural-signature embeddings · 2026-09-08