Analyze the pattern requirements

We need to find numbers (N) such that the sequence is Symbol (S) - Number (N) - Symbol (S). The sequence is: 2, 5, $, 8, 4, #, 7, 1, @, 3, 6, &, 9, 2, %, 4, 8,!, 5, 7.

Mapping the triplets

Let's examine the triplets: (2,5,$), (5,$,8), ($,8,4$), (8,4,#), (4,#,7), (#,7,1), (7,1,@), (1,@,3), (@,3,6), (3,6,&), (6,&,9), (&,9,2), (9,2,%), (2,%,4), (%,4,8), (4,8,!), (8,!,5), (!,5,7).

Verification of valid occurrences

Looking for S-N-S: (2,%,4) - here 2 is preceded by 9, not a symbol; (9,2,%) - 2 is between 9 and % (invalid); (%,4,8) - 4 is between % and 8 (invalid); (8,!,5) - 8 is between 4 and! (invalid); (!,5,7) - 5 is between! and 7 (invalid). Let's check (2,%,4) again: No. Check symbols in series: , #, @, &, \%,!. \text{Pattern} (S-N-S): 9 is followed by 2, but preceded by &. 2 is followed by \%, but preceded by 9. \text{Only} the triplet (!, 5, 7) - no. \text{Let}'s \text{look closely at the sequence}: 2 5 8 4 # 7 1 @ 3 6 & 9 2% 4 8! 5 7. Only '2' in the triplet '9 2%' is wrong. Wait, look at '9 2%' - 2 is preceded by 9 (digit), not symbol. Look at '2% 4' - 2 is a number, preceded by 9, followed by %. Check all numbers: 2, 5, 8, 4, 7, 1, 3, 6, 9, 2, 4, 8, 5, 7. Only one number '2' is preceded by '&' (if we had & 2%), but the sequence is & 9 2%. Actually, the only instance is '9 2%' - no. Let's re-verify: Is there any number surrounded by symbols? Scanning: 2, 5, $, 8, 4, #, 7, 1, @, 3, 6, &, 9, 2, %, 4, 8,!, 5, 7. There is no number between two symbols.