There is a series 8,7,6,5,6,7,8,7,6,7,8 which has local minima at 5 and 6.
How to get this using R?
library(zoo)
x <- c(8,7,6,5,6,7,8,7,6,7,8)
# eliminate runs
r <- rle(x)
r$lengths[] <- 1
xx <- inverse.rle(r)
xx[ rollapply(c(Inf, xx, Inf), 3, function(x) x[2] < min(x[-2])) ]
## [1] 5 6
If we knew that x had no runs, as is the case in the question's example, we could omit the three lines that eliminate runs and replace xx in the last statement with x. Use -Inf in place of both occurrences of Inf if you don't want to consider endpoints.
It is assumed that the input c(2, 1, 1, 3) should result in output of 1 once.