Array Initialisation Compile Time - Constexpr Sequence

I was reading this question on SO.

The question itself is not so interesting, but I was wondering whether it exists and how to implement a compile time solution.

Regard to the first sequence:

All numbers except the ones which can be divided by 3.

The sequence should be something like:

[1, 2, 4, 5, 7, 8, 10, 11, 13, 14, ...]

By induction, I've found the math formula for that sequence:

 f(0) = 0;
 f(x > 0) = floor[(3x - 1) / 2];

So I've implemented a C++ constexpr function which generates the i-th number in the sequence:

#include <type_traits>

template <typename T = std::size_t>
constexpr T generate_ith_number(const std::size_t index) {
  static_assert(std::is_integral<T>::value, "T must to be an integral type");

  if (index == 0) return 0;
  return (3 * index - 1) / 2;
}

Now I'd like to generate a "compile-time array/sequence" which stores the first N-th numbers of the sequence.

The structure should be something like:

template <typename T, T... values>
struct sequence {};

template <typename T, std::size_t SIZE>
struct generate_sequence {};  // TODO: implement

Questions (more than one, but related among them):

1) How to implement that kind of integer_sequence?

2) Is it possible to build an std::array from that integer_sequence at compile time?