A081837 -id:A081837 - cp's OEIS frontend

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).

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

Benoit Cloitre, Apr 11 2003

			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.

Cf. A001622, A081837 (for e), A373866 (for Pi).

A081836[n_] := Max[ContinuedFraction[Floor[GoldenRatio*10^n]/10^n]];
Array[A081836, 100, 0] (* Paolo Xausa, Jun 19 2024 *)

A373866 a(n) = maximum element in the continued fraction for Pi truncated to n decimal digits after the decimal point.

Original entry on oeis.org

3, 10, 7, 10, 14, 25, 84, 243, 288, 291, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 351, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292, 292

Offset: 0

Paolo Xausa, Jun 19 2024

			For n = 5, Pi truncated to 5 digits after the decimal point is 3.14159. The corresponding continued fraction is [3, 7, 15, 1, 25, 1, 7], whose maximum element is 25.

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

Cf. A000796, A001203, A081836 (analogous for phi), A081837 (analogous for e).

A373866[n_] := Max[ContinuedFraction[Floor[Pi*10^n]/10^n]];
Array[A373866, 100, 0]

cp's OEIS Frontend

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).

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