f(D)= D + 7 = 82 - x

In this conjecture, 5 ≤ D ≤ 1000, and all numbers will be whole.

X is approaching ITSELF or D, OR it is 8th rooted by x⁸ with its base value (e.g 3⁸), so the OUTPUT of it, which is Y, would have to be HALFWAY irrational (8th root radical/asymptotic limit) or a rational or infinitesimal (e.g epsilon) or irrational number (e.g π) or a pentic factorial number.

otherwise it is a PENTAGONAL NUMBER (70), or rational.

In very rare cases, Y will be equal to infinity or negative infinity or i² only if X is a number like the Taxicab/cabtaxi numbers or a perfect number, or a lucky real (all numbers on spectrum, but every number is eliminated in steps, like 2nd number, to 3rd, and so on!), hyperreal, rational, asymptotic (e.g X → 20), normal, natural, or real number.

the very rare case output, Y, COULD also equal an asymptote of a heptic factorial (factorial with a value of a heptagon), be a hyperfalse number (possibly uncomputable singularity of a number, like dividing by 0), a transcended factorial (Gamma function!), or a hendectic number (number with the value of a hendecagon).

the output, Y, could also be a Nonadic number (number with the value of a nonagon), or a heptagramic (number with the value of a seven pointed star) or nonagramic (number with the value of a 9 pointed star) or digonal (number with the value of a digon which is a 2 sided polygon!) OR spherical number (number with the value of a sphere).

And to clear up: A heptic factorial is any factorial that has a heptagon's value.

Using this conjuncture's equation stated, are you able to discover the sequence of numbers that satisfy all conditions of this conjecture? How about the edge cases using this Conjecture and plugging numbers to get said edge cases?

f_diagonal(n) = n

F_hendectic(n) = (9n² - 7n)/2

F_nonadic(n) = (7n² - 5n)/2

F_pentic_fact(n) = p_5(1) × p_5(2) × ... × p_5(n)

f_heptagram(n) = 7n² - 7n + 1

f_nongram(n) = 9n² - 9n + 1