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A081837 Let z(n) be e = exp(1.0) = 2.7182.... truncated to n decimal digits after the decimal point; sequence gives maximum element in the continued fraction for z(n).

%I A081837 #23 Jun 21 2024 14:18:23
%S A081837 2,3,4,12,9,10,12,11,9,10,8,22,13,13,15,12,35,30,48,18,166,166,68,40,
%T A081837 73,137,57,1288,62,28,416,552,138,47,24,156,110,31,463,85,108,106,295,
%U A081837 295,54,98,40,388,216,32,49,199,488,47,64,822,51,152,854,38,701,88,94,149
%N A081837 Let z(n) be e = exp(1.0) = 2.7182.... truncated to n decimal digits after the decimal point; sequence gives maximum element in the continued fraction for z(n).
%H A081837 Paolo Xausa, <a href="/A081837/b081837.txt">Table of n, a(n) for n = 0..10000</a>
%H A081837 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%e A081837 ... Here is Maple's computation of the first four terms of the sequence a:
%e A081837 ....C2 := 2
%e A081837 ....cf := [2]
%e A081837 ....a := [2]
%e A081837 ..........27
%e A081837 ....C2 := --
%e A081837 ..........10
%e A081837 ....cf := [2, 1, 2, 3]
%e A081837 ....a := [2, 3]
%e A081837 ..........271
%e A081837 ....C2 := ---
%e A081837 ..........100
%e A081837 ....cf := [2, 1, 2, 2, 4, 3]
%e A081837 ....a := [2, 3, 4]
%e A081837 ..........1359
%e A081837 ....C2 := ----
%e A081837 ..........500
%e A081837 ....cf := [2, 1, 2, 1, 1, 4, 1, 12]
%e A081837 ....a := [2, 3, 4, 12]
%p A081837 with(numtheory); Digits:=200:
%p A081837 C1 := exp(1.0);
%p A081837 for n from 1 to 100 do
%p A081837 C2:= floor(C1*10^(n-1))/10^(n-1);
%p A081837 cf := convert(evalf(C2),confrac):
%p A081837 a := [op(a),max(cf)];
%p A081837 od:
%p A081837 a; # _N. J. A. Sloane_, Jun 19 2024
%t A081837 A081837[n_] := Max[ContinuedFraction[Floor[E*10^n]/10^n]];
%t A081837 Array[A081837, 100, 0] (* _Paolo Xausa_, Jun 21 2024 *)
%Y A081837 Cf. A001113, A003417, A081836 (analogous for phi), A373866 (analogous for Pi).
%K A081837 base,nonn
%O A081837 0,1
%A A081837 _Benoit Cloitre_, Apr 11 2003
%E A081837 Definition, initial term, and offset clarified by _N. J. A. Sloane_, Jun 19 2024 following a suggestion from _Harvey P. Dale_.