A005531 Decimal expansion of fifth root of 2. (Formerly M3321)

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

1,3

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

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

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)

Example

1.148698354997035006798626946777927589443850889097797505513711118493603... - Harry J. Smith, May 12 2009

Mathematica

RealDigits[N[2^(1/5), 200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2012 *)

Prog

(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

Crossrefs

Cf. A002950 (continued fraction).

Cf. A002580 (cube root of 2).

Cf. A001622, A182007, A188593.

Sequence in context: A322087 A142350 A011515 * A328278 A288189 A335159

Adjacent sequences: A005528 A005529 A005530 * A005532 A005533 A005534

Keyword

nonn,cons

Author

N. J. A. Sloane

Extensions

More terms from Olaf Voß, Feb 13 2008

Status

approved