Exact prime-adic valuation conjecture

Prove or disprove that for every prime \(p\), the \(p\)-adic valuation of \(\consta(p)\) equals \(p-1\).

Background

The paper proves the lower bound $v_p(\consta(p))\ge p-1$ for prime pp and reports that the equality $v_p(\consta(p))=p-1$ holds for every tested prime through the available computational range.

The exact valuation is explicitly presented as a conjecture rather than a result. Establishing it would sharpen the known divisibility statement and explain a prominent regularity in the prime factorizations of the sequence.

References

For every prime p$, the $p$-adic valuation of \consta(p)$~is v_p\bigl(\consta(p)\bigr) \;=\; p - 1. In we establish %prove the lower bound $v_p\bigl(\consta(p)\bigr)\geqslant p-1$, yet we already see that it actually is exact. We shall report on our progress in the subsequent paper.

— New integer sequence OEIS A392714 counts Wronskians: fast evaluation via late-growing permutations  (2610.08636 - Shah et al., 6 Oct 2026) in Section 5.1, “Prime factorisations of known \(\consta(p)\),” Conjecture labeled conj:valuation