pi'ei'oi VUhU3 experimental cmavo

mathematical ternary operator: prime-generating function.

The a-th prime according to ordering rules b in ring c; contextless default for c is the standard/typical ring of integers (Z,+,*); contextless default for b is the standard typical ordering of the ring, which is the 'normal' absolute value (signless difference/distance with/from 0) for the standard ring (Z,+,*); thus, it will usually operate as an unary operator. The function must be defined over the set of strictly positive integers (or, more generally, ordinals) in/for the first operand; generalizations may be possible. Ignores units and 0. It begins counting at 1 in/for the first operand; under contextless default conditions, the outputs increase strictly monotonically with respect to increase in the first input [a], starting with the least prime in (Z,+,*), namely p_1 = 2. Usually denoted "p_i" or "Prime()" in the literature. See also: "fei'i", "pau'au".

In notes:

pau'au (exp!)
ternary mekso operator: p-adic valuation; outputs (positive) infinity if x1 = 0 and, else, outputs sup(Set(k: k is a nonnegative integer, and ((1 - x3)x divides x1)), where pn is the nth prime (such that p1 = 2).