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).

2, 3, 4, 12, 9, 10, 12, 11, 9, 10, 8, 22, 13, 13, 15, 12, 35, 30, 48, 18, 166, 166, 68, 40, 73, 137, 57, 1288, 62, 28, 416, 552, 138, 47, 24, 156, 110, 31, 463, 85, 108, 106, 295, 295, 54, 98, 40, 388, 216, 32, 49, 199, 488, 47, 64, 822, 51, 152, 854, 38, 701, 88, 94, 149

Offset: 0

Author

Benoit Cloitre, Apr 11 2003

Keywords

• base
• nonn

Examples

			... Here is Maple's computation of the first four terms of the sequence a:
....C2 := 2
....cf := [2]
....a := [2]
..........27
....C2 := --
..........10
....cf := [2, 1, 2, 3]
....a := [2, 3]
..........271
....C2 := ---
..........100
....cf := [2, 1, 2, 2, 4, 3]
....a := [2, 3, 4]
..........1359
....C2 := ----
..........500
....cf := [2, 1, 2, 1, 1, 4, 1, 12]
....a := [2, 3, 4, 12]
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• Index entries for continued fractions for constants

Crossrefs

Cf. A001113, A003417, A081836 (analogous for phi), A373866 (analogous for Pi).

Programs

Maple

with(numtheory); Digits:=200:
C1 := exp(1.0);
for n from 1 to 100 do
C2:= floor(C1*10^(n-1))/10^(n-1);
cf := convert(evalf(C2),confrac):
a := [op(a),max(cf)];
od:
a; # N. J. A. Sloane, Jun 19 2024

Mathematica

A081837[n_] := Max[ContinuedFraction[Floor[E*10^n]/10^n]];
Array[A081837, 100, 0] (* Paolo Xausa, Jun 21 2024 *)

Extensions

Definition, initial term, and offset clarified by N. J. A. Sloane, Jun 19 2024 following a suggestion from Harvey P. Dale.