cp's OEIS Frontend

A188485 Decimal expansion of (3+sqrt(17))/4, which has periodic continued fractions [1,1,3,1,1,3,1,1,3,...] and [3/2, 3, 3/2, 3, 3/2, ...].

%I A188485 #46 May 09 2025 19:12:27
%S A188485 1,7,8,0,7,7,6,4,0,6,4,0,4,4,1,5,1,3,7,4,5,5,3,5,2,4,6,3,9,9,3,5,1,9,
%T A188485 2,5,6,2,8,6,7,9,9,8,0,6,3,4,3,4,0,5,1,0,8,5,9,9,6,5,8,3,9,3,2,7,3,7,
%U A188485 3,8,5,8,6,5,8,4,4,0,5,3,9,8,3,9,6,9,6,5,9,1,2,7,0,2,6,7,1,0,7,4,1,7,1,1,3,6,0,1,0,2,3,4,8,0,3,5,3,5,4,0
%N A188485 Decimal expansion of (3+sqrt(17))/4, which has periodic continued fractions [1,1,3,1,1,3,1,1,3,...] and [3/2, 3, 3/2, 3, 3/2, ...].
%C A188485 Let R denote a rectangle whose shape (i.e., length/width) is (3+sqrt(17))/3.  This rectangle can be partitioned into squares in a manner that matches the continued fraction [1,1,3,1,1,3,1,1,3,...].  It can also be partitioned into rectangles of shape 3/2 and 3 so as to match the continued fraction [3/2, 3, 3/2, 3, 3/2, ...].  For details, see A188635.
%C A188485 Apart from the second digit the same as A188934. - _R. J. Mathar_, May 16 2011
%C A188485 Equivalent to the infinite continued fraction with denominators [1; 2, 1, 2, 1, ...] and numerators [2, 1, 2, ...], also expressible as 1+2/(2+1/(1+2/(2+1/...))). - _Matthew A. Niemiro_, Dec 13 2019
%H A188485 J. S. Brauchart, P. D. Dragnev, E. B. Saff, <a href="http://arxiv.org/abs/1402.3367">An Electrostatics Problem on the Sphere Arising from a Nearby Point Charge</a>, arXiv preprint arXiv:1402.3367 [math-ph], 2014. See Footnote 8. - _N. J. A. Sloane_, Mar 26 2014
%H A188485 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>.
%e A188485 1.780776406404415137455352463993519256287...
%t A188485 FromContinuedFraction[{3/2, 3, {3/2, 3}}]
%t A188485 ContinuedFraction[%, 25]  (* [1,1,3,1,1,3,1,1,3,...] *)
%t A188485 RealDigits[N[%%, 120]]  (* A188485 *)
%t A188485 N[%%%, 40]
%t A188485 RealDigits[(3+Sqrt[17])/4,10,120][[1]] (* _Harvey P. Dale_, May 09 2025 *)
%Y A188485 Cf. A188934, A246725.
%K A188485 nonn,cons
%O A188485 1,2
%A A188485 _Clark Kimberling_, May 05 2011