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a(n) = maximum element in the continued fraction for Pi truncated to n decimal digits after the decimal point.
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%I #34 Jan 06 2025 15:38:11

%S 3,10,7,10,14,25,84,243,288,291,292,292,292,292,292,292,292,292,292,

%T 292,292,292,292,292,292,292,292,292,292,292,292,292,292,292,292,351,

%U 292,292,292,292,292,292,292,292,292,292,292,292,292,292,292,292,292,292

%N a(n) = maximum element in the continued fraction for Pi truncated to n decimal digits after the decimal point.

%H Paolo Xausa, <a href="/A373866/b373866.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>

%e For n = 5, Pi truncated to 5 digits after the decimal point is 3.14159. The corresponding continued fraction is [3, 7, 15, 1, 25, 1, 7], whose maximum element is 25.

%t A373866[n_] := Max[ContinuedFraction[Floor[Pi*10^n]/10^n]];

%t Array[A373866, 100, 0]

%Y Cf. A000796, A001203, A081836 (analogous for phi), A081837 (analogous for e).

%K nonn,base,look

%O 0,1

%A _Paolo Xausa_, Jun 19 2024