The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A105172 Ultraradical of phi: decimal expansion of the real x such that x^5 + x = phi. 0
 9, 2, 8, 3, 8, 0, 7, 9, 9, 2, 5, 8, 9, 7, 4, 0, 2, 9, 5, 1, 4, 6, 5, 6, 0, 4, 4, 6, 6, 1, 2, 0, 7, 0, 1, 5, 1, 7, 7, 8, 3, 7, 0, 0, 6, 2, 8, 4, 4, 7, 0, 4, 2, 3, 6, 8, 0, 2, 1, 4, 8, 4, 0, 3, 3, 0, 5, 9, 4, 2, 4, 7, 0, 6, 9, 5, 9, 3, 7, 6, 7, 7, 2, 2, 1, 7, 7, 6, 8, 4, 8, 8, 9, 9, 0, 8, 0, 4, 0, 6 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Weisstein explains a term apparently coined by Ian Stewart: "Ultraradical: A symbol which can be used to express solutions not obtainable by finite root extraction. The solution to the irreducible quintic equation x^5 + x = a" can be written Ultraradical(a). We know from the classic papers by Abel and Galois of the unsolvability of the general quintic. The constant given here results from numerical evaluation of the irreducible quintic equation x^5 + x = phi. REFERENCES Birkhoff, G. and Mac Lane, S. "Insolvability of Quintic Equations." Section 15.8 in A Survey of Modern Algebra, 5th ed. New York: Macmillan, pp. 418-421, 1996. C. Runge, "Über die aufloesbaren Gleichungen von der Form x^5 + ux + v = 0", Acta Math. 7, 173-186, 1885. [German] S. R. Finch, "The Golden Mean." Section 1.2 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 5-12, 2003. LINKS Eric Weisstein's World of Mathematics, Ultraradical. Eric Weisstein's World of Mathematics, Quintic Equation. Eric Weisstein's World of Mathematics, Golden Ratio. FORMULA The decimal expansion of phi, the golden ratio, is given in A001622. EXAMPLE 0.928380799258974 CROSSREFS Cf. A001622. Sequence in context: A299957 A252001 A098784 * A231533 A011453 A125580 Adjacent sequences:  A105169 A105170 A105171 * A105173 A105174 A105175 KEYWORD cons,nonn AUTHOR Jonathan Vos Post, Apr 11 2005 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 21 21:30 EST 2020. Contains 331128 sequences. (Running on oeis4.)