A010770 Decimal expansion of 8th root of 2.

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

Offset

1,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Simon Plouffe, Numbers in the base e^Pi, 2025.

Index entries for algebraic numbers, degree 8.

Formula

Equals Product_{k>=0} (1 + (-1)^k/(8*k + 7)). - Amiram Eldar, Jul 29 2020

Empirical: Equals Sum_{k>=0} A080054(k) / exp(k*Pi). - Simon Plouffe, Sep 17 2025

Equals eta(i/2)/eta(i), where eta(t) denotes the Dedekind eta function, where i is the imaginary unit. - Peter Bala, May 28 2026

Mathematica

RealDigits[N[2^(1/8), 100]][[1]] (* Vincenzo Librandi, Apr 02 2013 *)

Prog

(PARI) sqrtn(2, 8) \\ Charles R Greathouse IV, Apr 15 2014

Crossrefs

Cf. A080054.

Cf. k-th root of 2: A002193 (k=2), A002580 (k=3), A010767 (k=4), A005531 (k=5), A010768-A010782 (k=6-20).

Sequence in context: A388917 A388471 A309605 * A388625 A021921 A388156

Adjacent sequences: A010767 A010768 A010769 * A010771 A010772 A010773

Keyword

nonn,cons,changed

Author

N. J. A. Sloane

Status

approved