Remove isolated elements of a vector

Question

I have a vector of integers and I want to filter it by eliminating the components that are "isolated". What do I mean by "isolated"? those components that does not lie in an 4-neighbourhood of other component. The components in the vector are ordered increasingly, and there are no repetitions.

For example if I have c(1,2,3,8,15,16,17) then I need to eliminate 8 because is not in a 4-neighbourhood of other element.

I've tried applying

   for (p in 1:(length(index)-2))
      if((index[p+1]>3+index[p])&(index[p+2]>3+index[p+1])){index[p+1]<-0}


    index<-index[index!=0]

where index is my vector of interest, but there's some problem with the logical condition. Could you please give me some hints?

Thanks in advance.

Answer 1

You can achieve it with a combination of outer and colSums, i.e.

x[colSums(abs(outer(x, x, `-`)) >= 4) == length(x)-1]
#[1] 8

To eliminate the values, we can do,

i1 <- colSums(outer(x, x, FUN = function(i, j) abs(i - j) >= 4)) == length(x) - 1
x[!i1]
#[1]  1  2  3 15 16 17

where,

x <- c(1,2,3,8,15,16,17)

Answer 2

We keep values where preceding or next difference is lower or equal to 4 :

v <- c(1,2,3,8,15,16,17)
v[c(FALSE, diff(v) <= 4) | c(diff(v) <= 4, FALSE)]