const mersenneSequenceNumber = x => 2 * x + 1; // f(x) = 2x + 1

function mersenneSequence(upTo = 10) {
  const list = [0]; // init with the first number

  // make the rest using the previous number in the list
  for (let i = 0; i < upTo; i++) {
    list.push(mersenneSequenceNumber(list[i]));
  }

  return list;
}

console.log(mersenneSequence()); // you can pass in a number, if not 10 is used
/*
[
    0,   1,    3,   7,
   15,  31,   63, 127,
  255, 511, 1023
]
*/