A188928 Decimal expansion of sqrt(12)+sqrt(13).

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

Offset

1,1

Comments

Decimal expansion of the length/width ratio of a sqrt(48)-extension rectangle. See A188640 for definitions of shape and r-extension rectangle.

A sqrt(48)-extension rectangle matches the continued fraction [7,14,2,1,4,21,3,9,1,4,2,1,1,1,2,...] for the shape L/W = sqrt(12)+sqrt(13). 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(48)-extension rectangle, 7 squares are removed first, then 14 squares, then 2 squares, then 1 square,..., so that the original rectangle of shape sqrt(12)+sqrt(13) is partitioned into an infinite collection of squares.

Links

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

Index entries for algebraic numbers, degree 4.

Formula

Minimal polynomial: x^4 - 50*x^2 + 1. - Amiram Eldar, May 31 2026

Example

7.0696528906017438801741139504822406801369...

Mathematica

r = 48^(1/2); t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]

Prog

(PARI) sqrt(12)+sqrt(13) \\ Charles R Greathouse IV, May 19 2026

Crossrefs

Cf. A188640, A188929.

Sequence in context: A196763 A321106 A225457 * A036479 A085966 A010678

Adjacent sequences: A188925 A188926 A188927 * A188929 A188930 A188931

Keyword

nonn,cons,changed

Author

Clark Kimberling, Apr 13 2011

Extensions

a(130) corrected by Georg Fischer, Apr 03 2020

Status

approved