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A190177 Decimal expansion of (1+sqrt(2)+sqrt(7+6*sqrt(2)))/2. 5
3, 1, 7, 4, 6, 7, 3, 8, 9, 4, 0, 3, 4, 1, 9, 8, 9, 2, 2, 9, 5, 8, 0, 7, 4, 4, 1, 2, 2, 1, 7, 2, 4, 3, 6, 4, 2, 9, 7, 4, 7, 8, 6, 1, 5, 8, 4, 1, 2, 1, 9, 6, 8, 7, 2, 9, 8, 3, 9, 9, 1, 1, 8, 5, 4, 1, 0, 0, 5, 5, 6, 5, 1, 4, 4, 6, 7, 5, 0, 7, 8, 7, 0, 3, 2, 2, 7, 3, 6, 2, 7, 3, 8, 2, 3, 0, 1, 0, 0, 7, 3, 9, 0, 6, 8, 1, 8, 5, 8, 2, 5, 9, 5, 1, 7, 6, 4, 3, 9, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Let R denote a rectangle whose shape (i.e., length/width) is (1+sqrt(2)+sqrt(7+6*sqrt(2)))/2. R can be partitioned into squares and silver rectangles in a manner that matches the periodic continued fraction [r,1,r,1,r,1,r,1,...], where r is the silver ratio: 1+sqrt(2)=[2,2,2,2,2,...]. R can also be partitioned into squares so as to match the nonperiodic continued fraction [3,5,1,2,1,1,1,2,...] at A190178. For details, see A188635.

LINKS

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

EXAMPLE

3.174673894034198922958074412217243642975...

MATHEMATICA

r = 1 + 2^(1/2));

FromContinuedFraction[{r, 1, {r, 1}}]

FullSimplify[%]

ContinuedFraction[%, 100]  (* A190178 *)

RealDigits[N[%%, 120]]     (* A190177 *)

N[%%%, 40]

RealDigits[(1+Sqrt[2]+Sqrt[7+6*Sqrt[2]])/2, 10, 100][[1]] (* G. C. Greubel, Dec 28 2017 *)

PROG

(PARI) (1+sqrt(2)+sqrt(7+6*sqrt(2)))/2 \\ G. C. Greubel, Dec 28 2017

(MAGMA) [(1+Sqrt(2)+Sqrt(7+6*Sqrt(2)))/2]; // G. C. Greubel, Dec 28 2017

CROSSREFS

Cf. A188635, A190178, A189970, A190179.

Sequence in context: A158841 A213576 A021319 * A283764 A010603 A269423

Adjacent sequences:  A190174 A190175 A190176 * A190178 A190179 A190180

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, May 05 2011

STATUS

approved

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Last modified November 13 11:22 EST 2018. Contains 317133 sequences. (Running on oeis4.)