ternary mekso operator: p-adic valuation; outputs (positive) infinity if x_{1 }= 0 and, else, outputs sup(Set(k: k is a nonnegative integer, and ((1 - x_{3)x} divides x_{1))}, where p_{n} is the nth prime (such that p_{1 }= 2).

The terbri order here was defined in analogy to "de'o". Normally, x_{1} should be a rational number, and x_{2} should be a positive integer; some generalizations may be possible, though. x_{3} is either 0 xor 1, and indicates/toggles between modes: x_{3 }= 0 yields the x_{2}-adic valuation (even for nonprime x_{2}); x_{3 }= 1 yields the p_{x}-adic valuation. x_{2 }= 1, x_{3 }= 0 yields positive infinity for any x_{1} which is within the domain. If x_{1 }= n/m and is a rational noninteger number such that gcd(n,m) = 1, then pau'au(x_{1, x}= pau'au(n, x_{2, x} pau'au(m, x_{2, x}. See also: "fei'i", "pi'ei'oi". This word is often equivalent to or closely related to "1 divided by X_{2} in algebraic structure X_{3}">pei'e'a" (which is, in some ways, more general but also is less flexible with respect to its input).

- fei'i
*(exp!)* - mekso variable-arity (at most ternary) operator: number of prime divisors of number X
_{1}, counting with or without multiplicity according to the value X_{2}(1 xor 0 respectively; see note for equality to -1 and for default value), in structure X_{3}. - pi'ei'oi
*(exp!)* - mathematical ternary operator: prime-generating function.