A173685 Decimal expansion of negative of previously unknown transition arising in exact dynamics for fully connected nonlinear network.

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

Offset

1,1

Comments

Given on p.3 of Tsironis. The paper has a major typo. Substituting N=3 into equation 16 produces the polynomial 108 - 43x +2x^2 + 2x^3, whose real zero is about -6.0399. The exact value is given in the formula below.

Links

Table of n, a(n) for n=1..150.

G. P. Tsironis, Exact dynamics for fully connected nonlinear networks, arXiv:1101.4721 Jan 25, 2011.

Formula

-(1 + f^(1/3)/2^(2/3) + 131/(2f)^(1/3))/3, where f=3307-387*sqrt(43).

Example

Chi_c ~ -6.03990424865074743952918719978407940028359436808....

Mathematica

RealDigits[Solve[108 - 43 x + 2 x^2 + 2 x^3 == 0, x][[1, 1, 2]], 10, 150][[1]]
r = (3307 - 387*Sqrt@ 43); RealDigits[-(1 + (r/4)^(1/3) + 131/(2r)^(1/3))/3, 10, 111][[1]] (* Robert G. Wilson v, Jan 31 2011 *)

Crossrefs

Sequence in context: A289487 A217708 A306243 * A019108 A019115 A229637

Adjacent sequences: A173682 A173683 A173684 * A173686 A173687 A173688

Keyword

nonn,cons

Author

Jonathan Vos Post, Jan 27 2011

Status

approved