Creating an integer column based on a specified length of time

[ConcernedPotatoe]

I am working with time series data and need to be able to sort it by week in order to create a facet graph. Using the following code, I have created a column with the week number of the year based on the Date_time column:

#Creates the Date_time column 
target_detections_all_15E$Date_time <- as.POSIXct(paste(as.Date(as.character(target_detections_all_15E$Ping_date),"%Y-%m-%d"), target_detections_all_15E$Ping_time, sep=" "),format = "%Y-%m-%d %H:%M:%S", tz="Asia/Bangkok")
#eliminates zeroes in the data
target_detections_all_15E<- target_detections_all_15E[target_detections_all_15E$TS_comp !=-9.9e+37,]
#Formats  the time to create the Week column and is supposed to change the week numbers to a sequence that starts at 1.
target_detections_all_15E$Week <- as.integer(format(target_detections_all_15E$Date_time, "%V"))
target_detections_all_15E<- transform(target_detections_all_15E, Week=Week-min(Week)+1)

Reprex data:

   Ping_date   Ping_time      Date_time      Week
1  2020-12-01  18:14:54 2020-12-01 18:14:54   49
2  2020-12-04  12:14:54 2020-12-04 12:14:54   49
3  2020-12-06  20:14:54 2020-12-06 20:14:54   49
4  2020-12-07  00:14:55 2020-12-07 00:14:55   50
5  2020-12-08  18:14:55 2020-12-08 18:14:55   50
6  2020-12-10  07:14:55 2020-12-10 07:14:55   50
7  2020-12-14  00:14:56 2020-12-14 00:14:56   51
8  2020-12-16  09:14:56 2020-12-16 09:14:56   51
9  2020-12-18  00:14:56 2020-12-18 00:14:56   51
10 2020-12-19  00:14:56 2020-12-19 00:14:56   51

My issue is that the number generated in the week column is based on the day and changes to "50" on 2020-12-07. My data starts at 2020-12-01 18:14:54 and I would like the week number to be dictated by a time range, in this case 168 hours after that initial start time so the end of week one becomes 2020-12-08 18:14:54. I need this to be set so that the Week column reads "1" up till 168 hours later and then switch to "2".

Example desired dataset:

   Ping_date   Ping_time      Date_time     Week
1  2020-12-01  18:14:54 2020-12-01 18:14:54   1
2  2020-12-04  12:14:54 2020-12-04 12:14:54   1
3  2020-12-08  17:14:54 2020-12-08 17:14:54   1
4  2020-12-08  18:14:55 2020-12-08 18:14:55   2
5  2020-12-10  18:14:55 2020-12-10 18:14:55   2
6  2020-12-15  17:14:55 2020-12-15 17:14:55   2
7  2020-12-15  18:14:56 2020-12-15 18:14:56   3
8  2020-12-17  18:14:56 2020-12-17 18:14:56   3
9  2020-12-18  18:14:56 2020-12-18 18:14:56   3
10 2020-12-20  18:14:56 2020-12-20 18:14:56   3

[FJCC]

I changed the date times to seconds and used integer division to count the weeks.

DF <- data.frame(DateTime = as.POSIXct(c("2020-12-01 18:14:54","2020-12-04  12:14:54", 
  "2020-12-08 17:14:54","2020-12-08 18:14:55","2020-12-10 18:14:55","2020-12-15 17:14:55",
  "2020-12-15 18:14:56","2020-12-17 18:14:56","2020-12-18 18:14:56","2020-12-20 18:14:56")))
DF$DateTimeNum <- as.numeric(DF$DateTime)
DF$DateTimeNum <- DF$DateTimeNum - as.numeric(as.POSIXct(c("2020-12-01 18:14:54")))
SecondsperWeek <- 168*3600
DF$Week <- DF$DateTimeNum %/% SecondsperWeek + 1
DF
#>               DateTime DateTimeNum Week
#> 1  2020-12-01 18:14:54           0    1
#> 2  2020-12-04 12:14:54      237600    1
#> 3  2020-12-08 17:14:54      601200    1
#> 4  2020-12-08 18:14:55      604801    2
#> 5  2020-12-10 18:14:55      777601    2
#> 6  2020-12-15 17:14:55     1206001    2
#> 7  2020-12-15 18:14:56     1209602    3
#> 8  2020-12-17 18:14:56     1382402    3
#> 9  2020-12-18 18:14:56     1468802    3
#> 10 2020-12-20 18:14:56     1641602    3

^{Created on 2021-08-11 by the reprex package (v0.3.0)}