10
$\begingroup$

A Sloane Sequence (or S-sequence) is any sequence of different positive integers begining with 1 in which the nth term (after the first) is the previous term plus n, times n, minus n, or divided by n (factorials are one such sequence: 1, 2, 6, 24...).

What is the earliest 2024 can occur in an S-sequence?

$\endgroup$

1 Answer 1

15
$\begingroup$

The best that I have done is

8

as follows

1, 3, 9, 36, 41, 246, 253, 2024

I think this is the best as

The highest we can get at position 6 is 1080 and, since 2024 is not divisible by 7, obtaining 2024 in 7 steps would require the last step not to be multiplication which is impossible.
As isaacg mentions in the comments, the largest possible number in step 7 not divisible by 7 is 1087.

$\endgroup$
2
  • 4
    $\begingroup$ To put the proof that 7 is impossible more concisely, 1087 is the largest number reachable in 7 steps that isn't a multiple of 7. $\endgroup$
    – isaacg
    Jan 15 at 18:00
  • 1
    $\begingroup$ Verified with recursive C program exploring each of the four operations for each term. $\endgroup$ Jan 15 at 20:20

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.