Erdős Problem #1204
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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A finite set `S` of natural numbers is *admissible* if it misses at least one residue class modulo every prime. A sequence \(0\leq a_1<\cdots <a_k\) is identified with the set of its values.
\(A(k)\): the least possible value of \(a_k\) over admissible sequences \(0\leq a_1<\cdots <a_k\). Any \(k\) primes larger than \(k\) form an admissible set, so `sInf` is a true minimum.
The least possible value of \(a_1+\cdots+a_k\) over admissible sequences \(0\leq a_1<\cdots <a_k\). As for `A`, the minimum exists.
Attempts
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proved the residue-vector and reflection reductions, exhaustively verified \(A(k)\), \(B(k)\), and greedy \(B\)-optimality for \(1\leq k\leq22\), and derived conditional liminf constants \(1/2\) and \
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