Stoneham number¶
In mathematics, the Stoneham numbers are a certain class of real numbers, named after mathematician Richard G.
Core Idea¶
Stoneham number is treated here as the recurring number theory identity summarized by this source-grounded definition: In mathematics, the Stoneham numbers are a certain class of real numbers, named after mathematician Richard G. In mathematics, the Stoneham numbers are a certain class of real numbers, named after mathematician Richard G. For coprime numbers b, c > 1, the Stoneham number α b,c is defined as. \alpha{b,c} = \sum{n=c^k>1} \frac{1}{b^nn} = \sum{k=1}^\infty \frac{1}{b{ck}c^k}.
Scope of Application¶
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Documented setting. In mathematics, the Stoneham numbers are a certain class of real numbers, named after mathematician Richard G.
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Documented setting. For coprime numbers b, c > 1, the Stoneham number α b,c is defined as.
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Documented setting. \alpha{b,c} = \sum{n=c^k>1} \frac{1}{b^nn} = \sum{k=1}^\infty \frac{1}{b{ck}c^k}.
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Documented setting. It was shown by Stoneham in 1973 that α b,c is b-normal whenever c is an odd prime and b is a primitive root of c 2 .
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Documented setting. In 2002, Bailey & Crandall showed that coprimality of b, c > 1 is sufficient for b-normality of α b,c .
Clarity¶
A clear use of Stoneham number names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In mathematics, the Stoneham numbers are a certain class of real numbers, named after mathematician Richard G.
Manages Complexity¶
Stoneham number compresses multiple number theory details into a stable diagnostic relation. The source shows both the central mechanism—in mathematics, the Stoneham numbers are a certain class of real numbers, named after mathematician Richard G.—and the practical consequence—it was shown by Stoneham in 1973 that α b,c is b-normal whenever c is an odd prime and b is a primitive root of c 2 .
Abstract Reasoning¶
- Type the carrier. Identify the number theory entities to which the claim applies.
- State the relation. Use the source-grounded identity: In mathematics, the Stoneham numbers are a certain class of real numbers, named after mathematician Richard G.
- Check operation and conditions. For coprime numbers b, c > 1, the Stoneham number α b,c is defined as.
- Demand recognition evidence. \alpha{b,c} = \sum{n=c^k>1} \frac{1}{b^nn} = \sum{k=1}^\infty \frac{1}{b{ck}c^k}. 5.
Knowledge Transfer¶
Within the home domain. Knowledge about Stoneham number transfers literally when a new case preserves the same carrier type, relation, and recognition test. In mathematics, the Stoneham numbers are a certain class of real numbers, named after mathematician Richard G. For coprime numbers b, c > 1, the Stoneham number α b,c is defined as. Beyond the home domain. No canonical parent is asserted for Stoneham number. An outside case receives the specialist name only when the same typed roles and rejection conditions can be filled literally; otherwise the comparison remains an analogy pending later graph densification.
Relationships to Other Abstractions¶
Current abstraction Stoneham number Domain-specific
Parents (1) — more general patterns this builds on
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Stoneham number is a kind of Normal Number Domain-specific
Stoneham numbers are the constructed real numbers whose entire mathematical significance is that they are provably normal to their base.
Hierarchy path (1) — routes to 1 parentless root
- Stoneham number → Normal Number → Convergence
Neighborhood in Abstraction Space¶
Stoneham number sits in a sparse region of the domain-specific corpus (78th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Algebraic Structures & Order Relations (18 abstractions)
Nearest neighbors
- Integral part — 0.84
- Binade — 0.83
- Coprime integers — 0.83
- Absolute value — 0.83
- Terminal singularity — 0.82
Computed from structural-signature embeddings · 2026-10-08