Generate series 1,2,1,3,2,1,4,3,2,1,5,4,3,2,1

Question

I am trying to generate a vector containing decreasing sequences of increasing length, such as 1, 2,1, 3,2,1, 4,3,2,1, 5,4,3,2,1, i.e.

c(1, 2:1, 3:1, 4:1, 5:1)

I tried to use a loop for this, but I don't know how to stack or concatenate the results.

for (i in 1:11)  {  x = rev(seq(i:1))  print(x)   } [1] 1 [1] 2 1 [1] 3 2 1 [1] 4 3 2 1 [1] 5 4 3 2 1 [1] 6 5 4 3 2 1 [1] 7 6 5 4 3 2 1 [1] 8 7 6 5 4 3 2 1 [1] 9 8 7 6 5 4 3 2 1 [1] 10  9  8  7  6  5  4  3  2  1 [1] 11 10  9  8  7  6  5  4  3  2  1 

I have also been experimenting with the rep, rev and seq, which are my favourite option but did not get far.

Answer 1

With sequence:

rev(sequence(5:1)) # [1] 1 2 1 3 2 1 4 3 2 1 5 4 3 2 1 

From R 4.0.0 sequence takes arguments from and by:

sequence(1:5, from = 1:5, by = -1) # [1] 1 2 1 3 2 1 4 3 2 1 5 4 3 2 1 

Far from the golf minimalism of rev... However, if you wake up one morning and want to create such a sequence with n = 1000 (like in the answer below), the latter is in fact faster (but I can hear Brian Ripley in fortunes::fortune(98))

n = 1000  microbenchmark(   f_rev = rev(sequence(n:1)),   f_seq4.0.0 = sequence(1:n, from = 1:n, by = -1)) # Unit: microseconds #        expr   min     lq     mean  median     uq    max neval #       f_rev 993.7 1040.3 1128.391 1076.95 1133.3 1904.7   100 #  f_seq4.0.0 136.4  141.5  153.778  148.25  150.1  304.7   100