A188932 - OEIS

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A188932

Decimal expansion of sqrt(7)+sqrt(8).

5, 4, 7, 4, 1, 7, 8, 4, 3, 5, 8, 1, 0, 7, 8, 0, 6, 8, 8, 1, 0, 4, 9, 9, 3, 2, 0, 2, 0, 5, 8, 6, 5, 6, 5, 8, 2, 8, 4, 9, 6, 0, 2, 9, 3, 3, 8, 3, 6, 3, 4, 6, 3, 2, 6, 7, 2, 1, 6, 9, 3, 9, 3, 5, 1, 8, 2, 5, 3, 3, 7, 8, 0, 1, 5, 4, 4, 9, 7, 7, 0, 5, 4, 6, 1, 1, 6, 7, 9, 5, 5, 1, 2, 9, 8, 2, 6, 7, 5, 6, 0, 8, 5, 0, 9, 2, 2, 7, 0, 8, 0, 0, 3, 2, 2, 0, 5, 7, 1, 4, 5, 5, 9, 3, 2, 0, 2, 0, 0, 0

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OFFSET

1,1

COMMENTS

Decimal expansion of the length/width ratio of a sqrt(28)-extension rectangle. See A188640 for definitions of shape and r-extension rectangle.

A sqrt(28)-extension rectangle matches the continued fraction [5,2,9,5,2,687,6,4,1,2,2,...] for the shape L/W=sqrt(7)+sqrt(8). 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 sqrt(28)-extension rectangle, 5 squares are removed first, then 2 squares, then 9 squares, then 5 squares,..., so that the original rectangle of shape sqrt(7)+sqrt(8) is partitioned into an infinite collection of squares.

LINKS

Table of n, a(n) for n=1..130.

EXAMPLE

5.47417843581078068810499320205865658284960293...

MATHEMATICA

r = 28^(1/2); t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]

N[t, 130]

RealDigits[N[t, 130]][[1]]

ContinuedFraction[t, 120]

RealDigits[Sqrt[7]+Sqrt[8], 10, 150][[1]] (* Harvey P. Dale, Jun 07 2017 *)

CROSSREFS

Cf. A188640, A188933.