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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).
3
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
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
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