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
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Apr 12 2011
STATUS
approved