an interesting take on Fibonacci numbers... For a change, Mathematica appears to be correct π
sage: k=12; (1/int((k-1)*"9"+"8"+k*"9")).n(4000)
1.00000000000100000000000200000000000300000000000500000000000800000000001300000000002100000000003400000000005500000000008900000000014400000000023300000000037700000000061000000000098700000000159700000000258400000000418100000000676500000001094600000001771100000002865700000004636800000007502500000012139300000019641800000031781100000051422900000083204000000134626900000217830900000352457800000570288700000922746500001493035200002415781700003908816900006324598600010233415500016558014100026791429600043349443700070140873300113490317000183631190300297121507300480752697600777874204901258626902502036501107403295128009905331629117308626757127213958386244522585143371736543529616259128672987995672202604254800875592250473078196505273953788755747031985261020985774016768017759277789003533294557021292572346024825866903046118439249070944306152117062745401188007051553305069796954493076848507798146645462291223493970089370139432380593633402469963772834850557406237320521179072171078585309491599764381662678349691154278114072816956463763971234577836788191041600759425619437547616661038307042280475854658941514161701221990016360163504178061385494194421548998372482934492566904483490939387417983506291901474445679319e-24