I think Robert Krzyzanowski is correct. So here is a tidyverse that involves placing the vector into a tibble (data frame).
library(tidyverse)
# library(dplyr)
# library(tidyr)
df <- c(1,2,3,4,5,19,20,21,56,80,81,92) %>%
tibble(dat = .)
# using lag()
df %>%
group_by(seq_id = cumsum(dat != lag(dat) + 1 | is.na(dat != lag(dat) + 1)) %>%
nest()
# using diff()
df %>%
group_by(seq_id = cumsum(c(1, diff(dat)) != 1)) %>%
nest()
Of course, you need not nest the resulting groups into list-columns, and can instead perform some kind of summary operation.