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A228497 Decimal expansion of the fourth root of 1/2.

%I A228497 #21 Mar 06 2025 05:37:20
%S A228497 8,4,0,8,9,6,4,1,5,2,5,3,7,1,4,5,4,3,0,3,1,1,2,5,4,7,6,2,3,3,2,1,4,8,
%T A228497 9,5,0,4,0,0,3,4,2,6,2,3,5,6,7,8,4,5,1,0,8,1,3,2,2,6,0,8,5,9,7,4,9,2,
%U A228497 4,7,5,4,9,5,3,9,0,2,2,3,9,8,1,4,3,2,4,0,0,4,1,9,9,2,9
%N A228497 Decimal expansion of the fourth root of 1/2.
%C A228497 Height of a equilateral square antiprism of edge length 1. - _R. J. Mathar_, Mar 06 2025
%H A228497 E. W. Weisstein, <a href="https://mathworld.wolfram.com/Antiprism.html">Antiprism</a>, MathWorld
%H A228497 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.
%F A228497 One divided by A010767.
%F A228497 Square root of A010503.
%F A228497 Equals Product_{k>=1} (1 + (-1)^k/(4*k+1)). - _Amiram Eldar_, Aug 10 2020
%e A228497 0.8408964152537145430311254762...
%p A228497 evalf(1/root[4](2)) ;
%t A228497 RealDigits[Surd[1/2,4],10,120][[1]] (* _Harvey P. Dale_, Oct 05 2014 *)
%o A228497 (PARI) sqrtn(2,-4) \\ _Charles R Greathouse IV_, Apr 15 2014
%Y A228497 Cf. A010503, A010767.
%K A228497 cons,nonn
%O A228497 0,1
%A A228497 _R. J. Mathar_, Aug 23 2013