A305992 The sequence whose indicator function is I in conjectured formula A300997(n) = 2*n - Sum_{k=1..n} I(k), as long as the conjecture holds.

1, 2, 4, 8, 15, 24, 32, 48, 62, 80, 101, 122, 147, 171, 202, 230, 267, 299, 339, 377, 418, 464, 509, 559, 611, 664, 719, 776, 836, 896, 960, 1024, 1098, 1167, 1240, 1315, 1392, 1471, 1553, 1642, 1724, 1816, 1906, 1999, 2094, 2190, 2290, 2392, 2499, 2599, 2713, 2818, 2937, 3048, 3166, 3288

Offset: 1

Author

Luc Rousseau, Jun 16 2018

Keywords

• nonn

Comments

A300997(n) is believed to be equal to 2*n - Sum_{k=1..n} I(k), where I is the indicator function of some other sequence -- let it be this sequence. This sequence is finite if the conjecture is false.

Links

• Wikipedia, Indicator function

Crossrefs

Cf. A300997.

Programs

C

#include 
#include 
#define N 10000
void e(int *t, int *s) {
  int T[N], i = 0; memset(T, 0, sizeof(T));
  while (i < *s) {
    int f = t[i] / 2;
    T[i] += f + (t[i] % 2);
    T[++ i] += f;
  }
  if (T[*s] != 0) { *s += 1; }
  for (i = 0; i < *s; i ++) { t[i] = T[i]; }
}
int f(int n) {
  int t[N], s = 1, i = 0; t[0] = n;
  while (s != n) { i ++; e(t, &s); }
  return 2 * n - i;
}
int main() {
  int n, last = 1, current;
  for (n = 1; n <= N; n ++) {
    current = f(n);
    switch (current - last) {
    case 0: break;
    case 1: printf("%d, ", n); fflush(stdout); break;
    default: fprintf(stderr, "CONJECTURE IS FALSE"); return;
    }
    last = current;
  }
  printf("\n");
}