A076392 Increasing partial quotients of the continued fraction for agm(1,i)/(1+i).
0, 1, 2, 42, 61, 88, 238, 254, 288, 347, 575, 4034, 9853, 21798, 49736, 108435, 109003, 181562, 1035352, 1955976, 6950275, 30712753, 41463747, 45117343, 112401242, 116579541
Offset: 1
Examples
A076391(1) = 0 A076391(2) = 1 A076391(4) = 2 A076391(5) = 42 A076391(96) = 61 A076391(121) = 88 A076391(310) = 238 A076391(461) = 254 A076391(540) = 288 A076391(627) = 347 A076391(699) = 575 A076391(1136) = 4034 A076391(2986) = 9853 A076391(4172) = 21798 A076391(16727) = 49736 A076391(39201) = 108435 A076391(110180) = 109003 A076391(130606) = 181562 A076391(506314) = 1035352 A076391(512390) = 1955976 A076391(1248836) = 6950275 A076391(1990391) = 30712753 A076391(2528055) = 41463747 A076391(4853400) = 45117343 A076391(7427594) = 112401242 A076391(96166990) = 116579541
Links
- Eric Weisstein's World of Mathematics, Arithmetic-Geometric Mean
- Wolfram Research, Arithmetic-Geometric Mean
Programs
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Mathematica
a = ContinuedFraction[ Chop[ N[ ArithmeticGeometricMean[1, I]/(1 + I), 10^4]]]; b = 0; Do[ If[ a[[n]] > b, Print[a[[n]]]; b = a[[n]]], {n, 1, 10^4}]
Extensions
a(21)-a(26) from Vaclav Kotesovec, Oct 03 2019