211 × 3
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072 and 6144
No.
Its nearest Fibonacci number neighbors are 4181 and 6765.