Explicit formulas are derived for v_3(s(a 3^n, k)) with a in {1,2} for all admissible k, proving the p=3 case of the Hong-Qiu conjecture.
Boyd, A p-adic study of the partial sums of the harmonic series, Experiment
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The 3-adic valuations of Stirling numbers of the first kind
Explicit formulas are derived for v_3(s(a 3^n, k)) with a in {1,2} for all admissible k, proving the p=3 case of the Hong-Qiu conjecture.