You could use something like a log
scaling to determine where you sample points from, e.g.:
x <- log(seq(1,100,length.out=24))
scx <- scale(x,center=min(x),scale=diff(range(x)))
out <- round(scx * length(sequence))
out[1] <- 1
sequence[out]
# [1] 1600 1749 1802 1836 1860 1879 1895 1908 1920 1930 1939 1948 1955
#[14] 1962 1969 1975 1981 1986 1991 1996 2001 2005 2009 2013
It's not exactly what you are asked for, but it approximates it. If you change the function to use something other than log
you may be able to get closer to your exact request.