A295330 Decimal expansion of sqrt(13)/2.

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

Offset: 1

Author

Wolfdieter Lang, Nov 20 2017

Keywords

• nonn
• cons

Comments

In a regular hexagon inscribed in a circle of radius R the largest distance between any vertex and a midpoint of a side, after division of R, is sqrt(13)/2. The two smaller distance ratios are sqrt(7)/2 = A242703 and 1/2.

The regular period 6 continued fraction of sqrt(13)/2 is [1; 1, 4, 14, 4, 1, 2], and the convergents are given in A295331/A295332.

Essentially the same as A223139, A209927, A098316 and A085550. - R. J. Mathar, Nov 23 2017

Examples

			1.8027756377319946465596106337352479731256482869226231063552265281135834741465...
		

Links

• Index entries for algebraic numbers, degree 2.

Crossrefs

Cf. A010470, A242703, A295331/A295332.

Programs

Mathematica

RealDigits[Sqrt@13/2, 10, 111][[1]] (* Robert G. Wilson v, Nov 20 2017 *)

PARI

sqrt(13)/2 \\ Michel Marcus, Nov 21 2017