remove individuals based on their range of values - r

Question

I have a df with two variables, one with IDs and one with a variable called numbers. I would like to excude individuals who do not start their sequence of numbers with the number 1.
I have managed to do this by creating a binary indicator and excluding if the person has this indicator. However, there must be a simpler more elegant way to do this?
Example data and the code I've used to achieve desired result are below.
Thank you.
sample df:
zz<-" names numbers
1 john 1
2 john 2
3 john 3
4 john 4
5 john 5
6 john 6
7 john 7
8 john 8
9 mary 4
10 mary 5
11 mary 6
12 mary 7
13 mary 8
14 mary 9
15 mary 10
16 mary 11
17 mary 12
18 pat 1
19 pat 2
20 pat 3
21 pat 4
22 pat 5
23 pat 6
24 pat 7
25 pat 8
26 pat 9
27 pat 10
28 sue 2
29 sue 3
30 sue 4
31 sue 5
32 sue 6
33 sue 7
34 sue 8
35 sue 9
36 tom 5
37 tom 6
38 tom 7
39 tom 8
40 tom 9
41 tom 10
42 tom 11
"
Data <- read.table(text=zz, header = TRUE)
Step 1 - add binary indicator
df$all<-ifelse(df$numbers==1, 1,0)
df$allperson<-ave(df$all, df$names, FUN=cumsum)
Step two - get rid of people who do not have 1 as their start number
df[!df$allperson==0,]

Answer 1

If you want elegance, I must recommend the package dplyr:
library(dplyr)
Data %>%
group_by(names) %>%
filter(min(numbers) != 1)
It means just what it appears to mean: filter only records where a group (defined by names) has a minimum numbers value inequal to 1.
names numbers
1 mary 4
2 mary 5
3 mary 6
4 mary 7
5 mary 8
6 mary 9
7 mary 10
8 mary 11
9 mary 12
10 sue 2
11 sue 3

Answer 2

You may also try:
zz1 <- zz[with(zz, names %in% unique(names)[!!table(zz)[,1]]),]
head(zz1,4)
# names numbers
#1 john 1
#2 john 2
#3 john 3
#4 john 4