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A188733 Decimal expansion of (9+sqrt(145))/8. 1
2, 6, 3, 0, 1, 9, 9, 3, 2, 2, 3, 4, 9, 0, 3, 6, 9, 3, 5, 0, 1, 6, 0, 3, 0, 1, 2, 8, 7, 9, 7, 3, 2, 6, 0, 0, 6, 5, 5, 3, 1, 6, 9, 0, 5, 0, 6, 3, 1, 7, 2, 9, 2, 4, 4, 0, 0, 9, 0, 5, 4, 1, 6, 5, 5, 6, 5, 8, 1, 1, 6, 4, 4, 1, 9, 5, 7, 2, 5, 8, 1, 8, 4, 3, 2, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Decimal expansion of shape of a (9/4)-extension rectangle; see A188640 for definitions of shape and r-extension rectangle. Briefly, shape=length/width, and an r-extension rectangle is composed of two rectangles of shape r. The (periodic) continued fraction of the constant is [2,1,1,1,2,2,1,1,1,2,2,1,...].
LINKS
EXAMPLE
2.6301993223490369350160301287973260065531690506317...
MAPLE
evalf((9+sqrt(145))/8, 120); # Muniru A Asiru, Nov 01 2018
MATHEMATICA
r = 9/4; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]
PROG
(PARI) (9+sqrt(145))/8 \\ Michel Marcus, Sep 03 2014
(Magma) SetDefaultRealField(RealField(100)); (9+Sqrt(145))/8; // G. C. Greubel, Nov 01 2018
CROSSREFS
Cf. A188640.
Sequence in context: A271503 A102068 A351709 * A104290 A152549 A136759
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Apr 10 2011
STATUS
approved

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Last modified March 29 09:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)