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A230242
Decimal expansion of (25+3*sqrt(69))/2.
0
2, 4, 9, 5, 9, 9, 3, 5, 7, 9, 4, 3, 7, 7, 1, 1, 2, 2, 7, 8, 8, 7, 6, 3, 9, 4, 1, 1, 7, 3, 6, 1, 2, 3, 8, 0, 1, 5, 3, 4, 8, 3, 2, 1, 3, 7, 3, 4, 3, 3, 4, 8, 3, 6, 6, 9, 1, 4, 8, 2, 8, 2, 5, 5, 3, 5, 5, 6, 3, 7, 7, 5, 5, 0, 1, 3, 4, 7, 2, 7, 3, 6, 0, 8, 0, 1
OFFSET
2,1
COMMENTS
Minimum mass ratio required for stable L4 and L5 Lagrange points. Because the mass of the sun is about 333060 times the mass of the earth which is greater than 24.95993..., the sun-earth Lagrange points L4 and L5 are stable. Similarly, since the earth is about 81.3 times more massive than the moon, the earth-moon L4 and L5 points are stable.
A quadratic integer with minimal polynomial x^2 - 25x + 1. - Charles R Greathouse IV, Mar 06 2015
Note that the L1, L2, and L3 Lagrangian points are unstable regardless of mass ratio. - Charles R Greathouse IV, Mar 25 2018
EXAMPLE
24.959935794377112278876394117361238015348321373433483669148282553556...
MATHEMATICA
First[RealDigits[(25 + 3*Sqrt[69])/2, 10, 100]] (* Paolo Xausa, Jun 18 2024 *)
PROG
(PARI) (25+3*sqrt(69))/2 \\ Charles R Greathouse IV, Oct 13 2013
(PARI) polrootsreal(x^2 - 25*x + 1)[2] \\ Charles R Greathouse IV, Jan 05 2016
CROSSREFS
Sequence in context: A301514 A269063 A161360 * A104654 A011182 A304753
KEYWORD
nonn,cons
AUTHOR
STATUS
approved