# Gah, these number sequences are just too boring!

Gah, these number sequences are just too boring! You just plug them in and then you're done!

There is a function $$f : \mathcal{S} \to \mathbb{Z}$$, where $$\mathcal{S}$$ is a finite subset of the positive integers that are $$10 \pmod{16}$$. It is known that $$f(59188506) = 127, ~f(101156906) = 108, ~f(51786282)=112, ~f(72562458)=97.$$

In addition, for many of the elements in $$\mathcal{S}$$, the value of $$f$$ is either zero or one.

What is $$f$$?

• Truly, a very nice "number sequence puzzle"! Feb 27, 2022 at 3:31

$$f(n)$$ is the function which
takes the hexadecimal representation of $$n$$, reverses it, and if the result is a valid A-number for an OEIS entry, returns the first member of the corresponding sequence.
$$59188506_{10} = 387251A_{16}$$, and A152783 begins $$\boxed{127}, 607, 4423, \dots$$
$$101156906_{10} = 607882A_{16}$$, and A288706 begins $$\boxed{108}, 614, 3840, \dots$$
$$51786282_{10} = 316322A_{16}$$, and A223613 begins $$\boxed{112}, 6592, 124672, \dots$$
$$72562458_{10} = 453371A_{16}$$, and A173354 begins $$\boxed{97}, 37840, 199652, \dots$$