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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 (list; constant; graph; refs; listen; history; text; internal format)
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 [math-ph], 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

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Last modified August 8 09:16 EDT 2020. Contains 336293 sequences. (Running on oeis4.)