A005531 Decimal expansion of fifth root of 2.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Comments

The sine of 2017 times this number is the near-integer 0.999999999999999978567771261.... - Alonso del Arte, May 03 2013

With the present number r = 2^(1/5) and the golden section phi = A001622 the other (complex) roots of x^5 - 2 are given by x1 = r*exp(2*Pi*i/5) = r*(phi - 1 + sqrt(2 + phi)*i)/2 = r*(A001622 - 1 + A188593*i)/2 = 0.3549673131... + 1.0924770557...*i, x2 = r*exp(4*Pi*i/5) = r*(-phi + sqrt(3 - phi)*i)/2 = r*(-A001622 + A182007*i)/2 = -0.9293164906... + 0.6751879523...*i, and their complex conjugates. - Wolfdieter Lang, Dec 06 2022

Examples

			1.148698354997035006798626946777927589443850889097797505513711118493603....
		

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• Index entries for algebraic numbers, degree 5.

Crossrefs

Cf. A002950 (continued fraction).

Cf. A002580 (cube root of 2).

Cf. A001622, A182007, A188593.

Programs

Mathematica

RealDigits[N[2^(1/5),200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2012 *)
RealDigits[Surd[2,5],10,120][[1]] (* Harvey P. Dale, May 08 2025 *)

PARI

{ default(realprecision, 20080); x=2^(1/5); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b005531.txt", n, " ", d)); } \\ Harry J. Smith, May 12 2009

Formula

Equals Product_{k>=0} (1 + (-1)^k/(5*k + 4)). - Amiram Eldar, Jul 25 2020

From Peter Bala, Mar 02 2022: (Start)

Equals (3/2)*Sum_{n >= 0} (1/(5*n+2) - 1/(5*n-3))*binomial(1/5,n). Cf. A002580.

Equals (5/4)*hypergeom([-1/5, -3/5], [7/5], -1). (End)

Extensions

More terms from Olaf Voß, Feb 13 2008