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%I M2231 #33 Feb 04 2024 03:23:45
%S 1,3,1,9,5,0,7,9,1,0,7,7,2,8,9,4,2,5,9,3,7,4,0,0,1,9,7,1,2,2,9,6,4,0,
%T 1,3,3,0,3,3,4,6,9,0,1,3,1,9,3,4,1,8,6,8,1,5,0,5,8,0,7,7,9,5,9,8,0,5,
%U 3,5,9,8,0,8,9,3,5,2,0,8,3,0,0,5,0,3,5
%N Decimal expansion of fifth root of 4.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Harry J. Smith, <a href="/A005533/b005533.txt">Table of n, a(n) for n = 1..20000</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>.
%F Equals Product_{k>=0} ((2*k+2)/(2*k+1))^((-3/2)^A000120(k)) (Allouche et al., 1987). - _Amiram Eldar_, Feb 04 2024
%e 1.319507910772894259374001971229640133033469013193418681505807795980535... - _Harry J. Smith_, May 11 2009
%t RealDigits[N[4^(1/5),200]][[1]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 22 2012 *)
%o (PARI) { default(realprecision, 20080); x=4^(1/5); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b005533.txt", n, " ", d)); } \\ _Harry J. Smith_, May 11 2009
%Y Cf. A000120, A003118 (continued fraction).
%K cons,nonn
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Jon E. Schoenfield_, Mar 11 2018
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