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A293506 Decimal expansion of real root of x^5 - x^4 - x^2 - 1.

%I A293506 #43 Feb 16 2025 08:35:42
%S A293506 1,5,7,0,1,4,7,3,1,2,1,9,6,0,5,4,3,6,2,9,1,0,6,6,5,4,3,5,1,3,7,1,2,6,
%T A293506 5,5,3,8,7,3,1,3,1,6,0,7,4,2,4,5,2,7,4,3,6,9,3,1,6,5,4,8,7,7,8,9,7,3,
%U A293506 3,0,6,6,1,5,4,4,1,6,2,3,2,0,2,2,2,7,6
%N A293506 Decimal expansion of real root of x^5 - x^4 - x^2 - 1.
%C A293506 This root is also the ninth smallest of the Pisot numbers.
%C A293506 The ratio of successive terms of A122115 converges to this number.
%H A293506 Iain Fox, <a href="/A293506/b293506.txt">Table of n, a(n) for n = 1..20000</a>
%H A293506 Hans Walser, <a href="http://www.walser-h-m.ch/hans/Miniaturen/F/Funktionenfolge/Funktionenfolge.pdf">Funktionenfolge</a> [in German]
%H A293506 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PisotNumber.html">Pisot Number</a>.
%H A293506 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pisot%E2%80%93Vijayaraghavan_number">Pisot-Vijayaraghavan number</a>
%H A293506 <a href="/index/Al#algebraic_05">Index entries for algebraic numbers, degree 5</a>
%e A293506 1.570147312196054362910665...
%t A293506 First@ RealDigits[Root[#^5 - #^4 - #^2 - 1 &, 1], 10, 87] (* _Michael De Vlieger_, Oct 23 2017 *)
%o A293506 (PARI) solve(x=1, 2, x^5 - x^4 - x^2 - 1) \\ _Michel Marcus_, Oct 11 2017
%o A293506 (PARI)  default(realprecision, 20080); x=solve(x=1, 2, x^5 - x^4 - x^2 - 1); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b293506.txt", n, " ", d));
%Y A293506 Cf. A060006, A086106, A228777, A092526, A293508, A293509, A293557, A122115, A293560 (inverse).
%K A293506 cons,nonn
%O A293506 1,2
%A A293506 _Iain Fox_, Oct 10 2017
%E A293506 More terms from _Andrey Zabolotskiy_, Oct 12 2017