A242703 Decimal expansion of sqrt(7)/2.

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

Offset: 1

Author

Alonso del Arte, May 20 2014

Keywords

• easy
• cons
• nonn

Comments

Absolute value of the imaginary part of any of the nontrivial divisors of 2 in O_Q(sqrt(-7)).

The incircle of a triangle with sides of lengths 4, 5, 6 units respectively has a radius of sqrt(7)/2.

With a different offset, decimal expansion of 5 * sqrt(7).

From Wolfdieter Lang, Nov 18 2017: (Start)

In a regular hexagon inscribed in a circle with a radius of 1 unit the three distinct distances between any vertex and the middle of the sides are 1/2, sqrt(7)/2 and sqrt(13)/2.

The continued fraction expansion of sqrt(7)/2 is 1, repeat(3, 10, 3, 2). The convergents are given in A294972/A294973. (End)

Examples

			1.32287565553229529525...
		

Links

• Iain Fox, Table of n, a(n) for n = 1..20000 (first 1000 terms from Ivan Panchenko)

Crossrefs

Cf. A010527, A020837, A040022, A294972/A294973.

Programs

Mathematica

RealDigits[Sqrt[7]/2, 10, 100][[1]]

PARI

{ default(realprecision, 20080); x=sqrt(7)/2; for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b242703.txt", n, " ", d)); } \\ Iain Fox, Nov 18 2017

Formula

(1/2 - sqrt(-7)/2)(1/2 + sqrt(-7)/2) = 2.

Equals A010465/2. - R. J. Mathar, Feb 23 2021