%I #26 Nov 08 2017 07:47:15
%S 1,5,0,1,5,9,4,8,0,3,5,3,9,0,8,7,3,6,6,3,7,7,7,8,3,1,2,7,3,7,1,0,4,6,
%T 1,0,8,4,8,6,3,9,8,3,3,6,2,5,3,5,8,5,3,4,2,2,4,8,3,9,4,1,8,6,0,6,3,3,
%U 4,3,6,1,2,5,9,7,1,2,8,8,9,8,1,3,4,1,1,4,2,4,6,0,2,9,2,0,0,2,0,1,7,2,5,5,8
%N Decimal expansion of the positive real root of x^6 - x^5 - x^4 + x^2 - 1.
%C This root is also the fifth smallest of the Pisot numbers.
%H Iain Fox, <a href="/A293508/b293508.txt">Table of n, a(n) for n = 1..20000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PisotNumber.html">Pisot Number</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Pisot%E2%80%93Vijayaraghavan_number">Pisot-Vijayaraghavan number</a>
%e 1.501594803539087366377783...
%t First@ RealDigits[Root[#^6 - #^5 - #^4 + #^2 - 1 &, 2], 10, 105] (* _Michael De Vlieger_, Oct 23 2017 *)
%o (PARI) solve(x=1, 2, x^6 - x^5 - x^4 + x^2 - 1) \\ _Michel Marcus_, Oct 11 2017
%o (PARI) { default(realprecision, 20080); x=solve(x=1, 2, x^6 - x^5 - x^4 + x^2 - 1); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b293508.txt", n, " ", d)); }
%Y Cf. A060006, A086106, A228777, A092526, A293506, A293509, A293557.
%K cons,nonn
%O 1,2
%A _Iain Fox_, Oct 11 2017