11
$\begingroup$

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 $f$?

$\endgroup$
1
  • $\begingroup$ Truly, a very nice "number sequence puzzle"! $\endgroup$ Feb 27, 2022 at 3:31

1 Answer 1

8
$\begingroup$

$f(n)$ 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.

Specifically,

$59188506_{10} = 387251A_{16}$, 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 $\boxed{97}, 37840, 199652, \dots$

$\endgroup$
1
  • $\begingroup$ That's it, great job! $\endgroup$
    – flame
    Feb 27, 2022 at 5:11

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.