<prompt> Fikiria mfululizo wa namba halisi chanya ya fomu x, 2000, y,... ambayo kila neno baada ya kwanza ni 1 chini ya bidhaa ya majirani wake wawili wa karibu. kwa thamani ngapi tofauti ya x neno 2001 inaonekana mahali fulani katika mfululizo?  <response>: Tuseme a, b, c ni masharti matatu mfululizo. Kisha b ac - 1, hivyo c b 1 a. Hebu a_n inaonyesha nth masharti. Kisha a_1 x, a_2 2000 na a_3 a_2 1 a_1 2001x, a_4 a_3 1 a_2 2001x 12000 x 20012000x, a_5 x 2001 2000x 1 2001x x 12000, a_6 x 12000 1 x 2001 2000x x, a_7 x 1 x 12000 2000. Kwa kuwa a_6 a_1 na a_7 a_2, na inategemea kipindi cha awali, tunaweza kuwa na mahesabu matano tu, ambayo yanaongoza kwa hatua ya kwanza, x 2001 2001 x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x 