turing machines – language in $R/NP$

I wondering whether the language $L_{hanoi} = {<k,s> | kin mathbb{N}textrm{ the number of rings and s is a sequence of legal solution of Tower of Hanoi problom}}$ is in $R/NP$

I want to claim that there is a turning machine that solves the problem, therefore, $L_{hanoi} in R$ but by a given solution to the problem to verify whether is a valid solution that takes $Omega (2^k)$
but it may be linear to the length of the input (number and sequence).

Anyway, where can I find examples for languages in $R/NP$?