You're searching for local maxima, essentially. Start off by normalizing your data to your target, i.e. 183, and search for values closest to zero. Those are your local maxima. I added data with values greater than your target to demonstrate.
df <- data.frame(DAYS = c(0,12,12,14,133,140,0,12,14,15,178,183,184,190,0,15,30,72,172,172.5))
df$localmin <- abs(df$DAYS - 183)
df
> df
    DAYS localmin
1    0.0    183.0
2   12.0    171.0
3   12.0    171.0
4   14.0    169.0
5  133.0     50.0
6  140.0     43.0
7    0.0    183.0
8   12.0    171.0
9   14.0    169.0
10  15.0    168.0
11 178.0      5.0
12 183.0      0.0
13 184.0      1.0
14 190.0      7.0
15   0.0    183.0
16  15.0    168.0
17  30.0    153.0
18  72.0    111.0
19 172.0     11.0
20 172.5     10.5
targets <- which(diff(sign(diff(c(df$localmin, 183)))) == 2) + 1L
df$targets <- 0
df$targets[targets] <- 1
df
> df
    DAYS localmin targets
1    0.0    183.0       0
2   12.0    171.0       0
3   12.0    171.0       0
4   14.0    169.0       0
5  133.0     50.0       0
6  140.0     43.0       1
7    0.0    183.0       0
8   12.0    171.0       0
9   14.0    169.0       0
10  15.0    168.0       0
11 178.0      5.0       0
12 183.0      0.0       1
13 184.0      1.0       0
14 190.0      7.0       0
15   0.0    183.0       0
16  15.0    168.0       0
17  30.0    153.0       0
18  72.0    111.0       0
19 172.0     11.0       0
20 172.5     10.5       1