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A081836
Let z(n) be the golden ratio (phi) truncated to n decimal digits; sequence gives maximum element in the continued fraction for z(n).
3
1, 2, 3, 5, 5, 6, 129, 15, 7, 10, 36, 65, 155, 70, 40, 20, 1122, 13, 15, 52, 52, 10, 19, 8, 87, 69, 42, 41, 30, 2036, 131, 86, 26, 41, 65, 231, 58, 161, 94, 94, 137, 137, 1323, 97, 14, 282, 15, 15, 122, 137, 80, 329, 164, 124, 748, 175, 7389, 2164, 101, 255, 201, 34, 17
OFFSET
0,2
EXAMPLE
phi=(1+sqrt(5))/2=1.6180339887498948482045... so z(10)=1.6180339887 and the continued fraction for z(10) is [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 2, 1, 1, 4, 1, 10, 36, 2], hence a(10)=36.
MATHEMATICA
A081836[n_] := Max[ContinuedFraction[Floor[GoldenRatio*10^n]/10^n]];
Array[A081836, 100, 0] (* Paolo Xausa, Jun 19 2024 *)
CROSSREFS
Cf. A001622, A081837 (for e), A373866 (for Pi).
Sequence in context: A326399 A192419 A376757 * A263721 A351259 A154290
KEYWORD
base,nonn
AUTHOR
Benoit Cloitre, Apr 11 2003
STATUS
approved