A188734 Decimal expansion of (7+sqrt(65))/4.

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

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 r-extension 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