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Search: id:A010469
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| A010469 |
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Decimal expansion of square root of 12. |
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+0
5
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| 3, 4, 6, 4, 1, 0, 1, 6, 1, 5, 1, 3, 7, 7, 5, 4, 5, 8, 7, 0, 5, 4, 8, 9, 2, 6, 8, 3, 0, 1, 1, 7, 4, 4, 7, 3, 3, 8, 8, 5, 6, 1, 0, 5, 0, 7, 6, 2, 0, 7, 6, 1, 2, 5, 6, 1, 1, 1, 6, 1, 3, 9, 5, 8, 9, 0, 3, 8, 6, 6, 0, 3, 3, 8, 1, 7, 6, 0, 0, 0, 7, 4, 1, 6, 2, 2, 9, 2, 3, 7, 3, 5, 1, 4, 4, 9, 7, 1, 5
(list; cons; graph; listen)
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OFFSET
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1,1
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COMMENT
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3+sqrt(12) is the ratio of the radii of the three identical kissing circles to that of their inner Soddy circle. - Lekraj Beedassy (blekraj(AT)yahoo.com), Mar 04 2006
sqrt(12)-3 = 2*sqrt(3)-3 is the area of the largest equilateral triangle that can be inscribed in a unit square (as stated in MathWorld/Weisstein link). - Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jun 24 2006
Continued fraction expansion is 3 followed by {2, 6} repeated. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 02 2009]
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,20000
Eric Weisstein's World of Mathematics, Equilateral Triangle.
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FORMULA
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a(n) = 2*sqrt(3) = 2*A002194. - Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jun 24 2006
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EXAMPLE
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3.4641016151377545870548926830...
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PROGRAM
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(PARI) { default(realprecision, 20080); x=sqrt(12); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010469.txt", n, " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 02 2009]
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CROSSREFS
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Cf. A040008.
Cf. A002194, A120683.
Cf. A040008 Continued fraction. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 02 2009]
Sequence in context: A065446 A159962 A055173 this_sequence A136248 A101432 A023823
Adjacent sequences: A010466 A010467 A010468 this_sequence A010470 A010471 A010472
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KEYWORD
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nonn,cons
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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