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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?

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15
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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.

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    $\begingroup$ 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
    Commented Jan 15 at 18:00
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    $\begingroup$ Verified with recursive C program exploring each of the four operations for each term. $\endgroup$
    – Weather Vane
    Commented Jan 15 at 20:20

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