Digit / CONCEPT
The Least Base Maximizing the Digit Sum Is the First Base Above Half
Past eight, the least base maximizing the digit sum of a number is the first base above half of it, because every base at most half loses more than half of the number to carries while the first base above half keeps all but half.
Closed
DIRECT PREREQUISITES0
DIRECT CONSEQUENCES2
PROOF DEPTH0
DOCUMENT LINKS1
The conjecture holds
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
None recorded in this release.
Certified topology / DOWNSTREAM
Consequences
RELATED KNOWLEDGE
Structural connections
- Asymptotic density of sets of naturalsstructural-affinity · Closed
- Bala's Alternating Gcd Sumstructural-affinity · Closed
- Digit-Sum Arcs: Infinitude and Natural Densitystructural-affinity · Closed
- Gupta's rectangular-grid dispersion inequalitystructural-affinity · Closed
- Integer {2}-domination of three-row gridsstructural-affinity · Closed
- Pillai mean and shared kernelsstructural-affinity · Closed
- The 2-neighbour bootstrap percolation number of C_n x P_m is nstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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