How to remove an unnamed element from a single item list?

Using nzchar.

lapply(v2, function(x) x[nzchar(x)])
# [[1]]
# [1] "1" "2" "3"

Or use base::strsplit in the first place which appears to be more sophisticated.

lapply(strsplit(v[[1]], ","), trimws)
# [[1]]
# [1] "1" "2" "3"

You can use Filter with nchar

v2 <- lapply(str_split(v, pattern = ",\\s?"), Filter, f = nchar)

which gives

> v2
[[1]]
[1] "1" "2" "3"

An option is also setdiff to remove the ""

lapply(str_split(v, pattern = ",\\s*"), setdiff, "")
#[[1]]
#[1] "1" "2" "3"

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