This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A160155 #34 Jul 17 2025 00:45:13
%S A160155 1,1,6,7,3,0,3,9,7,8,2,6,1,4,1,8,6,8,4,2,5,6,0,4,5,8,9,9,8,5,4,8,4,2,
%T A160155 1,8,0,7,2,0,5,6,0,3,7,1,5,2,5,4,8,9,0,3,9,1,4,0,0,8,2,4,4,9,2,7,5,6,
%U A160155 5,1,9,0,3,4,2,9,5,2,7,0,5,3,1,8,0,6,8,5,2,0,5,0,4,9,7,2,8,6,7,2,8,9,5,3,5
%N A160155 Decimal expansion of the one real root of x^5-x-1.
%C A160155 The other (complex) roots are 0.181232444469875383... + 1.08395410131771066...*i, and -0.764884433600584726... + 0.352471546031726249...*i, together with their complex conjugates. - _Wolfdieter Lang_, Dec 15 2022
%C A160155 This quintic is in some sense the smallest and/or simplest algebraic equation for which there is no explicit expression for the roots. (The "equivalent" quintic x^5 - x + 1 has the opposite real root, x = -1.1673..., while x^5 + x + 1 = (x^2 + x + 1)(x^3 - x^2 + 1).) - _M. F. Hasler_, Jul 12 2025
%H A160155 Harry J. Smith, <a href="/A160155/b160155.txt">Table of n, a(n) for n = 1..20000</a>
%H A160155 David W. Boys, <a href="http://dx.doi.org/10.1090/S0025-5718-1985-0790657-8">The maximal modulus of an algebraic integer</a>, Math. Comp. 45 (1985) 243-249, table page S18.
%H A160155 Wikipedia, <a href="https://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem">Abel-Ruffini theorem</a>, created Nov. 27, 2002, retrieved July 12, 2025.
%H A160155 Qiang Wu, <a href="http://dx.doi.org/10.1090/S0025-5718-10-02345-8">The smallest Perron numbers</a>, Math. Comp. 79 (2010) 2387-2394.
%H A160155 <a href="/index/Al#algebraic_05">Index entries for algebraic numbers, degree 5</a>
%F A160155 Equals (1 + (1 + (1 + (1 + (1 + ...)^(1/5))^(1/5))^(1/5))^(1/5))^(1/5). - _Ilya Gutkovskiy_, Dec 15 2017
%e A160155 1.16730397826141868425604589985484218072056037152548903914008244927565...
%t A160155 RealDigits[Root[x^5-x-1, x, 1], 10, 105] // First (* _Jean-François Alcover_, Jul 09 2015 *)
%o A160155 (PARI) localprec(20080); r=real(polroots('x^5 - 'x - 1)[1]); for (n=1, 20000, d=floor(r); r=(r-d)*10; write("b160155.txt", n, " ", d)) \\ Edited by _M. F. Hasler_, Jul 12 2025
%o A160155 (PARI) polrootsreal(x^5-x-1)[1] \\ _Charles R Greathouse IV_, Apr 14 2014
%Y A160155 Cf. A039922 (continued fraction), A001622 (golden ratio phi = root of x^2 - x - 1), A060006 (plastic constant, root of x^3 - x - 1), A060007 (root of x^4 - x - 1).
%K A160155 nonn,easy,cons
%O A160155 1,3
%A A160155 _Harry J. Smith_, May 03 2009