

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, ...].


4



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, 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, 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
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OFFSET

1,2


COMMENTS

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.
Apart from the second digit the same as A188485.  R. J. Mathar, May 16 2011
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


LINKS

Table of n, a(n) for n=1..120.
J. S. Brauchart, P. D. Dragnev, E. B. Saff, An Electrostatics Problem on the Sphere Arising from a Nearby Point Charge, arXiv preprint arXiv:1402.3367 [mathph], 2014. See Footnote 8.  N. J. A. Sloane, Mar 26 2014


EXAMPLE

1.780776406404415137455352463993519256287...


MATHEMATICA

FromContinuedFraction[{3/2, 3, {3/2, 3}}]
ContinuedFraction[%, 25] (* [1, 1, 3, 1, 1, 3, 1, 1, 3, ...] *)
RealDigits[N[%%, 120]] (* A188485 *)
N[%%%, 40]


CROSSREFS

Cf. A188485.
Sequence in context: A181438 A088396 A199723 * A093828 A010514 A073004
Adjacent sequences: A188482 A188483 A188484 * A188486 A188487 A188488


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, May 05 2011


STATUS

approved



