It is not exactly the supefunction of zeration (max-kroenecker delta definition)...but it is the superfunction of Bennett's base 2 preaddition (-1th rank in base 2 commutative hos hierarchy).

In fact you are right: define plusation (set it as rank 1 of a new sequence)

Let's take it's subfunction in the variable x (i.e. where )

But the sequence doesn't seem much interesting or natural imho... the only nice properties are that

1) it is based on the usual recursion/iteration law (ML )

2) it intersects the 2-based commutative hos sequence at t=0 ()

In fact you are right: define plusation (set it as rank 1 of a new sequence)

Let's take it's subfunction in the variable x (i.e. where )

But the sequence doesn't seem much interesting or natural imho... the only nice properties are that

1) it is based on the usual recursion/iteration law (ML )

2) it intersects the 2-based commutative hos sequence at t=0 ()

MathStackExchange account:MphLee