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

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?

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.

• 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. Commented Jan 15 at 18:00
• Verified with recursive C program exploring each of the four operations for each term. Commented Jan 15 at 20:20