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 A046965 Cos(a(n)) decreases monotonically to -1. 6
 1, 2, 3, 22, 355, 104348, 208341, 521030, 833719, 1146408, 5419351, 85563208, 165707065, 245850922, 657408909, 1068966896, 3618458675, 6167950454, 21053343141, 1804419559672, 3587785776203, 5371151992734, 14330089761671, 130796280757852 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS May be computed found using convergents to the continued fraction for Pi. If cos(a(n)) is near -1, then a(n) is near an odd multiple of Pi. That is, a(n)/(2k+1) is a good rational approximation to Pi with an odd denominator (and continued fractions give good rational approximations). If a convergent of the continued fraction for Pi has an odd denominator then the corresponding numerator is a term in this sequence. Otherwise add one to the last term in the convergent to get an approximation of Pi with an odd denominator. In this case, we may get a duplicate of the next convergent which we may just ignore. To illustrate: [3] = 3/1 -> 3; [3,7] = 22/7 -> 22; [3,7,15] = 333/106; 106 is even -> [3,7,16] = 355/113 -> 355; [3,7,15,1] = 355/113 -> 355 (ignore); [3,7,15,1,292] = 103993/33102 -> [3,7,15,1,293] = 104348/33215 -> 104348 LINKS MATHEMATICA z={}; current=1; Timing[ Do[ If[ Cos[ n ]

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Last modified February 29 05:25 EST 2020. Contains 332353 sequences. (Running on oeis4.)