How to generate a Sequence From a Given sequence

I am trying to generate a sequence

for Example as shown below ::

> s
[1]  1  5  7 10 

>s.Generated_Seq 
[1]  1 2 9 10 13 14 19 20 

> s
[1]  2 5 7 10 

>s.Generated_Seq 
[1]  3 4 9 10 13 14 19 20 

Note : when sequence is started from 1 its generated sequence should start from 1 only and if sequence is started from 2 or 6 or 15 or any number generated sequence should be multiple of that number.

We can create a function that takes a vector as input argument and returns the transformed output based on the logic described

f1 <- function(vec){
  if(vec[1]==1) {  #if the first element is 1
   #append the first element with the twice multiplied other elements
      c(vec[1], 2*vec[-1]) 
   #or else just multiply the vector with the first element
  } else vec*vec[1]
 }

f1(v1)
#[1]  1 10 14 20

f1(v2)
#[1]  4 10 14 20

data

v1 <- c(1, 5, 7, 10)
v2 <- c(2, 5, 7, 10)