0
$\begingroup$

I have thought up a sequence, and I name it the nice and round sequence. Its first 10 numbers are

15773, 29694, 165083, 276316, 496325, 498512, 702504, 719466, 808667, 826245

What is its pattern?


Hint 1:

More numbers of the sequence can be found in this spreadsheet https://docs.google.com/spreadsheets/d/150JlMSb_Fd6v4z2wElkdYTgo54e8CiBWS1pP0pnp4X4/edit?usp=sharing

Hint 2:

I do not think there is a formula to compute the terms.

Hint 3:

What number is considered nice by the internet denizens? What number is related to round things?

$\endgroup$
7
  • 2
    $\begingroup$ Does Hint 2 imply that the sequence is uncomputable, or simply mean that there isn't an arithmetic formula? (Related: a small set of arithmetic operations can cover very wide range of computable functions) $\endgroup$
    – Bubbler
    Feb 4, 2021 at 1:00
  • $\begingroup$ @Bubbler It can be found using a computer program, but there is no explicit formula (I think), just like the sequence of primes numbers, which there is no formula to compute it but you may write a program to find prime numbers. $\endgroup$ Feb 4, 2021 at 12:52
  • 2
    $\begingroup$ Okay, that answers my question. Btw, people have come up with purely arithmetic formula for primality testing and such, so "there's no formula to compute it" is quite stronger statement than it sounds. $\endgroup$
    – Bubbler
    Feb 4, 2021 at 13:24
  • $\begingroup$ @Bubbler Primality testing is not quite the same as a formula that generates the sequence of prime numbers. Somehow relevant is this wiki page where there are some interesting formulas, both recurrent and non-recurrent. $\endgroup$
    – WhatsUp
    Feb 5, 2021 at 19:14
  • $\begingroup$ Hint 3 makes me think of fvkgl-avar (gur "avpr" zrzr) naq cv vf trarenyyl eryngrq gb pvepyrf but so far no luck making it work :< $\endgroup$
    – Pepper
    Feb 6, 2021 at 8:50

1 Answer 1

3
$\begingroup$

The pattern is made up of the

positions of the sequence 69420 (nice) within the digits of Pi after the decimal place (round).

The next number in the sequence (excluding those in the hint within the question) is

3022306, as the 3022306th, 3022307th, ... and 3022310th digits of Pi after the decimal place are 69420.

$\endgroup$

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.