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%I #38 Feb 23 2021 10:55:15
%S 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,
%T 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,
%U 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
%N Decimal expansion of sqrt(7)/2.
%C Absolute value of the imaginary part of any of the nontrivial divisors of 2 in O_Q(sqrt(-7)).
%C The incircle of a triangle with sides of lengths 4, 5, 6 units respectively has a radius of sqrt(7)/2.
%C With a different offset, decimal expansion of 5 * sqrt(7).
%C From _Wolfdieter Lang_, Nov 18 2017: (Start)
%C 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.
%C The continued fraction expansion of sqrt(7)/2 is 1, repeat(3, 10, 3, 2). The convergents are given in A294972/A294973. (End)
%H Iain Fox, <a href="/A242703/b242703.txt">Table of n, a(n) for n = 1..20000</a> (first 1000 terms from Ivan Panchenko)
%F (1/2 - sqrt(-7)/2)(1/2 + sqrt(-7)/2) = 2.
%F Equals A010465/2. - _R. J. Mathar_, Feb 23 2021
%e 1.32287565553229529525...
%t RealDigits[Sqrt[7]/2, 10, 100][[1]]
%o (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
%Y Cf. A010527, A020837, A040022, A294972/A294973.
%K easy,cons,nonn
%O 1,2
%A _Alonso del Arte_, May 20 2014
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