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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 (3-sqrt(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

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Last modified April 15 19:43 EDT 2021. Contains 342977 sequences. (Running on oeis4.)