Closely related, but different from this solved quesion
Let $\zeta^{(k)}(s)$ denote the $k$-th derivative of Riemann zeta function. For real $x$, let $[x]$ denote the nearest integer to $x$.
Conjecture 1: For integer $B \ge 2$ we have $[\zeta^{(1)}(1-1/B)]=[\zeta^{(1)}(1+1/B)]$
Conjecture 2: Let $k=1$ or $k=2$. Then $[\zeta^{(k)}(1-1/B)]= -B^{k+1}\cdot k!$
According to computations with mpmath and pari/gp, both hold up to 10^5 for integer $B$.
From the linked question, $k=41$ violates generalization of (2).
