A197592 Decimal expansion of least x>0 having (cos(x))^2+(sin(2x))^2=1/2.

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

Offset

1,2

Comments

For a discussion and guide to related sequences, see A197739.

Links

Table of n, a(n) for n=1..99.

Index entries for transcendental numbers.

Example

1.2333519040018934291489892079836642261607...

Mathematica

(See the program at A197589.)
RealDigits[ ArcCos[ Sqrt[ (5-Sqrt[17])/2 ]/2 ], 10, 99] // First (* Jean-François Alcover, Feb 27 2013 *)

Prog

(PARI) solve(x=1, 2, cos(x)^2+sin(2*x)^2-.5) \\ Charles R Greathouse IV, Apr 19 2026
(PARI) 2*atan(polrootsreal(x^8 + 28*x^6 - 74*x^4 + 28*x^2 + 1)[3]) \\ Charles R Greathouse IV, Apr 19 2026
(PARI) acos(sqrt((5-sqrt(17))/2)/2) \\ Charles R Greathouse IV, Apr 19 2026

Crossrefs

Cf. A197739, A197589.

Sequence in context: A171628 A205566 A064338 * A103359 A020481 A066660

Adjacent sequences: A197589 A197590 A197591 * A197593 A197594 A197595

Keyword

nonn,cons

Author

Clark Kimberling, Oct 18 2011

Status

approved