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A190256 Decimal expansion of sqrt((3 + x + sqrt(9+6x))/2), where x=sqrt(6). 2
2, 2, 7, 1, 2, 8, 1, 5, 6, 2, 4, 2, 2, 9, 9, 4, 1, 4, 2, 3, 1, 3, 0, 5, 8, 0, 6, 8, 7, 5, 9, 7, 2, 6, 8, 5, 5, 4, 5, 5, 8, 4, 9, 2, 6, 9, 1, 0, 2, 1, 4, 3, 4, 3, 2, 8, 7, 4, 9, 0, 8, 2, 8, 2, 6, 5, 9, 1, 6, 4, 3, 9, 1, 5, 4, 3, 9, 2, 2, 1, 2, 3, 6, 1, 6, 7, 1, 5, 1, 8, 5, 5, 1, 0, 2, 9, 6, 0, 3, 1, 3, 7, 3, 1, 9, 7, 0, 3, 3, 5, 9, 4, 8, 5, 3, 0, 0, 5, 2, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The rectangle R whose shape (i.e., length/width) is sqrt(3+x+sqrt(9+6x)), where x=sqrt(6), can be partitioned into rectangles of shapes sqrt(3) and sqrt(2) in a manner that matches the periodic continued fraction [sqrt(3), sqrt(2), sqrt(3), sqrt(2), ...]. R can also be partitioned into squares so as to match the nonperiodic continued fraction [2,3,1,2,5,2,1,5,95,1,...] at A190257. For details, see A188635.
LINKS
EXAMPLE
2.271281562422994142313058068759726855455...
MATHEMATICA
FromContinuedFraction[{3^(1/2), 2^(1/2), {3^(1/2), 2^(1/2)}}]
FullSimplify[%]
ContinuedFraction[%, 100] (* A190256 *)
RealDigits[N[%%, 120]] (* A190257 *)
N[%%%, 40]
PROG
(PARI) sqrt((3+sqrt(6)+sqrt(9+6*sqrt(6)))/2) \\ G. C. Greubel, Dec 26 2017
(Magma) [Sqrt((3+Sqrt(6)+Sqrt(9+6*Sqrt(6)))/2)]; // G. C. Greubel, Dec 26 2017
CROSSREFS
Sequence in context: A198880 A201315 A199861 * A013671 A019807 A362029
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, May 06 2011
EXTENSIONS
Name corrected by T. D. Noe, Feb 25 2013
STATUS
approved

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)