|
| |
|
|
A105171
|
|
Ultraradical of e. Decimal expansion of the real x such that x^5 + x = e.
|
|
0
| |
|
|
1, 1, 0, 0, 9, 3, 2, 6, 6, 5, 1, 9, 3, 6, 2, 6, 6, 0, 7, 6, 5, 4, 9, 7, 5, 8, 8, 0, 2, 6, 1, 4, 0, 8, 3, 6, 0, 8, 4, 1, 1, 8, 4, 8, 2, 8, 0, 1, 9, 4, 6, 5, 1, 6, 1, 8, 1, 3, 6, 2, 0, 7, 4, 5, 6, 8, 5, 9, 9, 6, 8, 1, 4, 5, 2, 0, 6, 2, 4, 9, 7, 6, 1, 7, 1, 2, 5, 2, 1, 4, 4, 8, 5, 7, 0, 5, 0, 1, 6, 1
(list; constant; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,5
|
|
|
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 = e.
|
|
|
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, "Ueber die aufloesbaren Gleichungen von der Form x^5 + ux + v = 0", Acta Math. 7, 173-186, 1885. [German]
|
|
|
LINKS
| Eric Weisstein's World of Mathematics, Ultraradical.
Eric Weisstein's World of Mathematics, Quintic Equation.
Eric Weisstein's World of Mathematics, e.
|
|
|
FORMULA
| The decimal expansion of e is given in A001113.
|
|
|
EXAMPLE
| 1.10093266519...
|
|
|
MATHEMATICA
| RealDigits[x/.FindRoot[x^5+x==E, {x, 1.1}, WorkingPrecision->150]][[1]] (* From Harvey P. Dale, Mar 09 2011 *)
|
|
|
CROSSREFS
| Cf. A001113.
Sequence in context: A072559 A019941 A200624 * A010538 A019721 A201320
Adjacent sequences: A105168 A105169 A105170 * A105172 A105173 A105174
|
|
|
KEYWORD
| cons,nonn
|
|
|
AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 11 2005
|
| |
|
|
