A010767 Decimal expansion of 4th root of 2.

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

Offset

1,3

Comments

An algebraic integer of degree 4. - Charles R Greathouse IV, Nov 12 2014

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 5.23, p. 407.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Jean-Paul Allouche, Henri Cohen, Michel Mendès France, and Jeffrey O. Shallit, De nouveaux curieux produits infinis, Acta Arithmetica, Vol. 49, No. 2 (1987), pp. 141-153; alternative link.

Simon Plouffe, 2^(1/4) or sqrt(sqrt(2)) to 20000 digits.

Simon Plouffe, 2^(1/4) to 1024 places.

Nikita Sidorov and Boris Solomyak, On the topology of sums in powers of an algebraic number, arXiv:0909.3324 [math.NT], 2009-2011.

David Terr and Eric W. Weisstein, Pisot Number.

Index entries for algebraic numbers, degree 4.

Formula

Equals Product_{k>=0} (1 + (-1)^k/(4*k + 3)). - Amiram Eldar, Jul 25 2020

Equals Product_{k>=0} ((2*k+1)/(2*k+2))^(A000120(k)*(-1)^A000120(k)) (Allouche et al., 1987). - Amiram Eldar, Feb 04 2024

Example

1.189207115002721066717499970560475915292972092...

Mathematica

RealDigits[N[2^(1/4), 200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jan 24 2012 *)

Prog

(PARI) sqrtn(2, 4) \\ Charles R Greathouse IV, Apr 14 2014
(PARI) weber(I) \\ Charles R Greathouse IV, Feb 04 2015

Crossrefs

Cf. A000120, A228497 (the multiplicative inverse).

Sequence in context: A113521 A297537 A030167 * A334751 A289252 A064734

Adjacent sequences: A010764 A010765 A010766 * A010768 A010769 A010770

Keyword

nonn,cons,easy

Author

N. J. A. Sloane

Status

approved