A358938 Decimal expansion of the real root of 2*x^5 - 1.

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

Offset: 0

Author

Wolfdieter Lang, Dec 07 2022

Keywords

• nonn
• cons
• easy

Comments

This is the reciprocal of A005531.

The other two complex conjugate pairs of roots are obtained, with the present number r = (1/2)^(1/5) and the golden section phi (A001622), from x1 = r*exp(Pi*i*2/5) = r*(phi - 1 + sqrt(2 + phi)*i)/2 = r*(A001622 - 1 + A188593*i)/2 = 0.2690149185... + 0.8279427859...*i, x2 = r*exp(Pi*i*4/5) = r*(-phi + sqrt(3 - phi)*i)/2 = r*(-A001622 + A182007*i)/2 = -0.7042902001... + 0.5116967824...*i.

Examples

			0.87055056329612413913627001747974609897912542434800304824185956850675...
		

Crossrefs

Cf. A001622, A182007, A188593, A005531, A011101.

Programs

Mathematica

RealDigits[Surd[1/2, 5], 10, 120][[1]] (* Amiram Eldar, Dec 07 2022 *)

Formula

r = (1/2)^(1/5) = 1/A005531.

Equals A011101/2. - Hugo Pfoertner, Mar 24 2025