

A192938


Decimal expansion of the real positive root of the equation: 4*d^4 + 12*d^3 + 8*d^2  1 = 0.


0



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

0,1


COMMENTS

If the side lengths of a triangle form a harmonic progression in the ratio 1 : 1/(1+d) : 1/(1+2d) where d is the common difference between the denominators of the harmonic progression, then when d = 0.290772978969... it forms a unique right triangle. The angles (in degrees) are approximately 39.2195, 50.7805, 90.


LINKS

Table of n, a(n) for n=0..98.


FORMULA

d as given by the real positive root of 4*d^4 + 12*d^3 + 8*d^2  1 = 0.


EXAMPLE

0.29077297896941138371325966971645222964831895500614673035846014851282...


MATHEMATICA

N[Reduce[1+8d^2+12d^3+4d^4==0, d], 100]
RealDigits[x/.FindRoot[4x^4+12x^3+8x^21==0, {x, .2}, WorkingPrecision> 120]][[1]] (* Harvey P. Dale, Feb 15 2015 *)


PROG

(PARI) polrootsreal(4*x^4+12*x^3+8*x^21)[2] \\ Charles R Greathouse IV, Apr 15 2014


CROSSREFS

Sequence in context: A221245 A340009 A021348 * A188619 A020817 A245217
Adjacent sequences: A192935 A192936 A192937 * A192939 A192940 A192941


KEYWORD

easy,nonn,cons


AUTHOR

Frank M Jackson, Aug 02 2011


STATUS

approved



