A246825 Decimal expansion of the Narcissus constant, the second real solution of the equation x^(x-1) = x+1.

2, 3, 9, 8, 3, 8, 4, 3, 8, 2, 7, 8, 1, 6, 1, 1, 4, 2, 9, 3, 9, 3, 8, 7, 6, 8, 4, 7, 5, 2, 3, 8, 7, 4, 1, 9, 1, 8, 0, 6, 9, 9, 1, 7, 7, 5, 1, 6, 2, 5, 6, 2, 8, 2, 8, 1, 9, 6, 9, 1, 1, 1, 0, 7, 9, 4, 4, 8, 7, 7, 9, 7, 4, 1, 2, 1, 6, 4, 1, 6, 2, 3, 4, 6, 4, 1, 4, 5, 1, 5, 4, 4, 6, 6, 1, 6, 5, 9, 5, 3, 0, 9, 4

Offset

1,1

Comments

The narcissus constant is defined as a number that satisfies a "narcissistic" infinite nested radical equation (see the link).

Links

Table of n, a(n) for n=1..103.

Jean-François Alcover, Narcissus constant defined with nested radicals

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 57.

Teik-Cheng Lim, Potential energy function based on the narcissus constant, its square and its cube, J. Math. Chem. 43 (2008) 304—313; MR2449420.

Example

2.398384382781611429393876847523874191806991775162562828...

Mathematica

digits = 103; x /. FindRoot[x^(x - 1) == x + 1, {x, 2}, WorkingPrecision -> digits + 5] // RealDigits[#, 10, digits]& // First

Crossrefs

Sequence in context: A299773 A021421 A152812 * A378330 A086565 A008291

Adjacent sequences: A246822 A246823 A246824 * A246826 A246827 A246828

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 04 2014

Status

approved