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A242703
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Decimal expansion of sqrt(7)/2.
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4
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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
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OFFSET
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1,2
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COMMENTS
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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).
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)
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LINKS
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FORMULA
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(1/2 - sqrt(-7)/2)(1/2 + sqrt(-7)/2) = 2.
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EXAMPLE
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1.32287565553229529525...
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MATHEMATICA
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RealDigits[Sqrt[7]/2, 10, 100][[1]]
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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