

A178255


Decimal expansion of (3+sqrt(17))/2.


6



3, 5, 6, 1, 5, 5, 2, 8, 1, 2, 8, 0, 8, 8, 3, 0, 2, 7, 4, 9, 1, 0, 7, 0, 4, 9, 2, 7, 9, 8, 7, 0, 3, 8, 5, 1, 2, 5, 7, 3, 5, 9, 9, 6, 1, 2, 6, 8, 6, 8, 1, 0, 2, 1, 7, 1, 9, 9, 3, 1, 6, 7, 8, 6, 5, 4, 7, 4, 7, 7, 1, 7, 3, 1, 6, 8, 8, 1, 0, 7, 9, 6, 7, 9, 3, 9, 3, 1, 8, 2, 5, 4, 0, 5, 3, 4, 2, 1, 4, 8, 3, 4, 2, 2, 7
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Continued fraction expansion of (3+sqrt(17))/2 is A109007.
a(n) = A082486(n) for n > 1.
The rectangle R whose shape (i.e., length/width) is (3+sqrt(17))/2 can be partitioned into rectangles of shapes 3 and 3/2 in a manner that matches the periodic continued fraction [3, 3/2, 3, 3/2, ...]. R can also be partitioned into squares so as to match the periodic continued fraction [3, 1, 1, 3, 1, 1,...]. For details, see A188635.  Clark Kimberling, May 07 2011
The positive eigenvalue of the real symmetric 2 X 2 matrix M defined by M(i,j) = max(i,j) = [(1 2), (2 2)] is (3+sqrt(17))/2, while the negative one is (3sqrt(17))/2. For a generalization, see A085984.  Bernard Schott, Apr 13 2020
A quadratic integer with minimal polynomial x^2  3x  2.  Charles R Greathouse IV, Apr 14 2020


LINKS

Table of n, a(n) for n=1..105.


EXAMPLE

(3+sqrt(17))/2 = 3.56155281280883027491...


MATHEMATICA

FromContinuedFraction[{3, 3/2, {3, 3/2}}]
ContinuedFraction[%, 100] (* [3, 1, 1, 3, 1, 1, ...] *)
RealDigits[N[%%, 120]] (* A178255 *)
N[%%%, 40]
(* Clark Kimberling, May 07 2011 *)


PROG

(PARI) (3+sqrt(17))/2 \\ Charles R Greathouse IV, Apr 14 2020


CROSSREFS

Cf. A082486 (decimal expansion of (5+sqrt(17))/2), A010473 (decimal expansion of sqrt(17)), A109007 (repeat 3, 1, 1), A085984.
Sequence in context: A111950 A274792 A243589 * A154467 A152713 A218802
Adjacent sequences: A178252 A178253 A178254 * A178256 A178257 A178258


KEYWORD

cons,nonn


AUTHOR

Klaus Brockhaus, May 24 2010


STATUS

approved



