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).

%I A081836 #9 Jun 21 2024 08:38:35
%S A081836 1,2,3,5,5,6,129,15,7,10,36,65,155,70,40,20,1122,13,15,52,52,10,19,8,
%T A081836 87,69,42,41,30,2036,131,86,26,41,65,231,58,161,94,94,137,137,1323,97,
%U A081836 14,282,15,15,122,137,80,329,164,124,748,175,7389,2164,101,255,201,34,17
%N 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).
%e A081836 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.
%t A081836 A081836[n_] := Max[ContinuedFraction[Floor[GoldenRatio*10^n]/10^n]];
%t A081836 Array[A081836, 100, 0] (* _Paolo Xausa_, Jun 19 2024 *)
%Y A081836 Cf. A001622, A081837 (for e), A373866 (for Pi).
%K A081836 base,nonn
%O A081836 0,2
%A A081836 _Benoit Cloitre_, Apr 11 2003