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A188731
Decimal expansion of (5+sqrt(41))/4.
1
2, 8, 5, 0, 7, 8, 1, 0, 5, 9, 3, 5, 8, 2, 1, 2, 1, 7, 1, 6, 2, 2, 0, 5, 4, 4, 1, 8, 6, 5, 5, 4, 5, 3, 3, 1, 6, 1, 3, 0, 1, 0, 5, 0, 3, 3, 1, 5, 5, 2, 5, 4, 7, 2, 1, 3, 8, 2, 3, 1, 8, 1, 5, 6, 6, 6, 7, 0, 4, 5, 6, 8, 9, 5, 4, 9, 2, 1, 9, 0, 1, 8, 5, 7, 2, 3, 3, 8, 5, 7, 5, 5, 6, 2, 4, 6, 7, 4, 9, 0, 7, 9, 2, 7, 0, 2, 9, 5, 8, 1, 2, 5, 9, 4, 9, 2, 9, 5, 8, 1, 5, 6, 1, 7, 4, 3, 6, 0, 9, 3
OFFSET
1,1
COMMENTS
Decimal expansion of shape of a (5/2)-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 continued fractions of the constant are 2, 1, 5, 1, 2, 2, 1, 5, 1, 2, 2, 1, 5, 1, 2, 2, 1, 5, 1...
LINKS
EXAMPLE
2.850781059358212171622054418655453316130105033155254721...
MAPLE
evalf((5+sqrt(41))/4, 140); # Muniru A Asiru, Nov 01 2018
MATHEMATICA
r = 5/2; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]
PROG
(PARI) default(realprecision, 100); (5+sqrt(41))/4 \\ G. C. Greubel, Nov 01 2018
(Magma) SetDefaultRealField(RealField(100)); (5+Sqrt(41))/4; // G. C. Greubel, Nov 01 2018
CROSSREFS
Cf. A188640.
Sequence in context: A011058 A368644 A229981 * A188617 A154157 A197150
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Apr 10 2011
STATUS
approved