Lucky number¶
A natural number surviving an iterative positional sieve that repeatedly deletes every kth remaining number.
Core Idea¶
Lucky numbers begin with the positive integers, remove every second number, then use each next surviving number as the deletion step for the remaining sequence. Successive rank-based eliminations produce an infinite increasing set whose construction resembles the prime sieve but depends on current positions rather than divisibility. 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.
The load-bearing residual is not the broad topic of number theory. It is the domain-specific identity determined by the number remains after every deletion stage of the standard lucky-number sieve with the stated starting convention.
Scope of Application¶
Lucky number belongs to number theory and is useful where the analyst can specify the typed number theory carrier, defining objects and relations, parameters, conventions, evidence, boundary cases and comparison targets, then evaluate the number remains after every deletion stage of the standard lucky-number sieve with the stated starting convention. The scope is broad within that domain but bounded by the need for the number remains after every deletion stage of the standard lucky-number sieve with the stated starting convention. 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 number remains after every deletion stage of the standard lucky-number sieve with the stated starting convention 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 Lucky 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 Lucky number. Lucky 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 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 number remains after every deletion stage of the standard lucky-number sieve with the stated starting convention independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of number theory because they reuse the typed number theory carrier, defining objects and relations, parameters, conventions, evidence, boundary cases and comparison targets, Successive rank-based eliminations produce an infinite increasing set whose construction resembles the prime sieve but depends on current positions rather than divisibility., and type the carrier, state every parameter and convention in the definition, test that the number remains after every deletion stage of the standard lucky-number sieve with the stated starting convention, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Lucky number Domain-specific
Parents (1) — more general patterns this builds on
-
Lucky number is a kind of Recursion Prime
The proposed strict upward parent is
prime:recursion.
Hierarchy path (1) — routes to 1 parentless root
- Lucky number → Recursion
Neighborhood in Abstraction Space¶
Lucky number sits in a crowded region of the domain-specific corpus (14th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Number-Theoretic Sequences & Classes (37 abstractions)
Nearest neighbors
- Complete sequence — 0.92
- Unusual number — 0.92
- Highly composite number — 0.92
- Prime triplet — 0.92
- Brun sieve — 0.92
Computed from structural-signature embeddings · 2026-09-08