

A188734


Decimal expansion of (7+sqrt(65))/4.


3



3, 7, 6, 5, 5, 6, 4, 4, 3, 7, 0, 7, 4, 6, 3, 7, 4, 1, 3, 0, 9, 1, 6, 5, 3, 3, 0, 7, 5, 7, 5, 9, 4, 2, 7, 8, 2, 7, 8, 3, 5, 9, 9, 0, 7, 6, 4, 0, 2, 1, 4, 3, 3, 4, 6, 9, 8, 4, 1, 4, 8, 0, 9, 7, 3, 1, 5, 9, 6, 8, 7, 3, 7, 7, 5, 6, 4, 2, 2, 0, 5, 0, 7, 4, 0, 0, 3, 8, 5, 6, 6, 6, 7, 9, 3, 0, 7, 6, 6, 0, 9, 0, 9, 3, 6, 0, 6, 1, 6, 5, 3, 4, 9, 8, 6, 4, 7, 8, 0, 5, 3, 4, 3, 7, 1, 6, 3, 0, 3, 0
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OFFSET

1,1


COMMENTS

Apart from the second digit, the same as A171417.  R. J. Mathar, Apr 15 2011
Apart from the first two digits, the same as A188941.  Joerg Arndt, Apr 16 2011
Decimal expansion of the length/width ratio of a (7/2)extension rectangle. See A188640 for definitions of shape and rextension rectangle.
A (7/2)extension rectangle matches the continued fraction [3,1,3,3,1,3,3,1,3,3,1,3,3,...] for the shape L/W=(7+sqrt(65))/4. This is analogous to the matching of a golden rectangle to the continued fraction [1,1,1,1,1,1,1,1,...]. Specifically, for the (7/2)extension rectangle, 3 squares are removed first, then 1 square, then 3 squares, then 3 squares,..., so that the original rectangle of shape (7+sqrt(65))/4 is partitioned into an infinite collection of squares.


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000


EXAMPLE

3.7655644370746374130916533075759427827835990...


MAPLE

evalf((7+sqrt(65))/4, 140); # Muniru A Asiru, Nov 01 2018


MATHEMATICA

r = 7/2; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]


PROG

(PARI) default(realprecision, 100); (7+sqrt(65))/4 \\ G. C. Greubel, Nov 01 2018
(MAGMA) SetDefaultRealField(RealField(100)); (7+Sqrt(65))/4; // G. C. Greubel, Nov 01 2018


CROSSREFS

Cf. A188640.
Sequence in context: A157699 A283270 A159779 * A021883 A338065 A278818
Adjacent sequences: A188731 A188732 A188733 * A188735 A188736 A188737


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Apr 12 2011


STATUS

approved



