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

0,1

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Index entries for continued fractions for constants

Example

... 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]

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 *)

Crossrefs

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

Sequence in context: A373576 A013620 A317498 * A119799 A036779 A037339

Adjacent sequences: A081834 A081835 A081836 * A081838 A081839 A081840

Keyword

base,nonn

Author

Benoit Cloitre, Apr 11 2003

Extensions

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

Status

approved