Infinite Motel

[Jack Brennen]

I tried to look at extending/analyzing the sequence, but I hit a problem
right away...  I come up with a slightly different sequence (which I'm
sure diverges greatly as you continue):

You show:
  1,2,13,3,6,26,4,11,408,9,5,24,7,51,22,102,20,49,18,8,205,10,16,...
I show:
  1,2,13,3,6,26,4,11,205,9,5,24,7,51,22,102,20,49,18,8,410,10,16,...
                     ^^^                               ^^^

Here's my C code, if anyone wants to run it themselves, or look
for errors in my implementation...

#include <stdio.h>
#include <stdlib.h>

#define XLIM 100000

static unsigned rooms[XLIM];

int main(void)
{
  unsigned door=1;
  unsigned label=1;
  unsigned cnt;
  unsigned n;

  for (;;) {
    printf("Room %u gets label %u\n", door, label);
    rooms[door] = label;
    for (cnt=0, n=door-1; n; n--)
      if (rooms[n]==0)
        if (++cnt == label)
          break;
    if (n) {
      door = n;
      ++label;
      continue;
    }
    for (cnt=0, n=door+1; n<XLIM; n++)
      if (rooms[n]==0)
        if (++cnt == label)
          break;
    if (n<XLIM) {
      door = n;
      ++label;
      continue;
    }
    break;
  }
  printf("done\n");

  return EXIT_SUCCESS;
}