From Catalin Francu
C++ source code that generates A005228.

Runs in (approx.) O( n + sqrt(n) + sqrt(sqrt(n)) + sqrt(sqrt(sqrt(n)))...) 
to generate the first n elements. Tested up to n = 1,000,000,000. 
Input is n, output is a(n). Needs quasi-constant memory.

%o A005228 #include <stdio.h>

typedef unsigned long long uint64;

typedef struct {
  uint64 value;
  uint64 inc;
} pair;

pair series[100];

void init_all_series() {
  pair initial_pair = { 7, 5 }; // pregenerate the first three terms
  for (int i = 0; i < 99; series[i++] = initial_pair);
}

void generate(int k);

inline bool test(int k, unsigned number) {
  switch (number) {
    case 1: case 3: case 7: return 1;
    case 2: case 4: case 5: case 6: return 0;
    default:
      while (series[k].value < number) generate(k);
      return (series[k].value == number);
  }
}

inline void generate(int k) {
  series[k].value += series[k].inc;
  if (test(k+1, ++series[k].inc)) series[k].inc++;
}

int main(void) {
  int x;

  init_all_series();
  scanf("%d", &x); // Enter the index
  switch (x) {
    case 1: puts("1"); break;
    case 2: puts("3"); break;
    default:
      for (int k = 4; k <= x; k++) generate(0);
      printf("%llu
", series[0].value); // print the x'th term
  }
  return 0;
}