Le Monde puzzle [#854]

A Le Monde mathematical puzzle that sounds similar to earlier ones:

Find all integers x between 1000 and 9999 and N≥1 such Nx has the reverse sequence of digits compared with i.  

For N=1, the appropriate integers x are such that the four digits are symmetrical, as in x=3553. For N≥1, I ran the following R code:

for (i in 10^3:(5*10^3)){
 dig=rev(intToDigits(i))
 for (N in 2:8){
  if (N*i>9999) break()
  if (max(abs(intToDigits(N*i)-dig))<.1)
      print(c(i,N,N*i))
      }}

and only found the single entry

[1] 2178    4 8712

where the intToDigits function was suggested to me by Pierre Pudlo:

intToDigits <- function(x) {
 if (length(x) != 1) {
   warning( "x should be of length 1. Using only x[1]")
   x <- x[1]
   }
 m <- floor(log10(x)) + 1
 pow10 <- 10^(1:m)
 xpow <- x * pow10 / (10^m)
 xrep <- trunc(xpow) / pow10
 digits <- c(xrep[1], xrep[-1]-xrep[-m]) * pow10
 digits
 }