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%I #61 Feb 04 2024 03:24:27
%S 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,
%T 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,
%U 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
%N Decimal expansion of 4th root of 2.
%C An algebraic integer of degree 4. - _Charles R Greathouse IV_, Nov 12 2014
%H Vincenzo Librandi, <a href="/A010767/b010767.txt">Table of n, a(n) for n = 1..1000</a>
%H Jean-Paul Allouche, Henri Cohen, Michel Mendès France, and Jeffrey O. Shallit, <a href="https://doi.org/10.4064/aa-49-2-141-153">De nouveaux curieux produits infinis</a>, Acta Arithmetica, Vol. 49, No. 2 (1987), pp. 141-153; <a href="https://eudml.org/doc/206075">alternative link</a>.
%H Simon Plouffe, <a href="http://www.plouffe.fr/simon/constants/sqrsqrt2.txt">2^(1/4) or sqrt(sqrt(2)) to 20000 digits</a>.
%H Simon Plouffe, <a href="https://web.archive.org/web/20080205212939/https://worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap83.html">2^(1/4) to 1024 places</a>.
%H Nikita Sidorov and Boris Solomyak, <a href="http://arxiv.org/abs/0909.3324">On the topology of sums in powers of an algebraic number</a>, arXiv:0909.3324 [math.NT], 2009-2011.
%H David Terr and Eric W. Weisstein, <a href="http://mathworld.wolfram.com/PisotNumber.html">Pisot Number</a>.
%H <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.
%F Equals Product_{k>=0} (1 + (-1)^k/(4*k + 3)). - _Amiram Eldar_, Jul 25 2020
%F Equals Product_{k>=0} ((2*k+1)/(2*k+2))^(A000120(k)*(-1)^A000120(k)) (Allouche et al., 1987). - _Amiram Eldar_, Feb 04 2024
%e 1.18920711...
%t RealDigits[N[2^(1/4),200]][[1]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 24 2012 *)
%o (PARI) sqrtn(2,4) \\ _Charles R Greathouse IV_, Apr 14 2014
%o (PARI) weber(I) \\ _Charles R Greathouse IV_, Feb 04 2015
%Y Cf. A000120, A228497 (the multiplicative inverse).
%K nonn,cons
%O 1,3
%A _N. J. A. Sloane_
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