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A244593 Decimal expansion of z_c = phi^5 (where phi is the golden ratio), a lattice statistics constant which is the exact value of the critical activity of the hard hexagon model. 1
1, 1, 0, 9, 0, 1, 6, 9, 9, 4, 3, 7, 4, 9, 4, 7, 4, 2, 4, 1, 0, 2, 2, 9, 3, 4, 1, 7, 1, 8, 2, 8, 1, 9, 0, 5, 8, 8, 6, 0, 1, 5, 4, 5, 8, 9, 9, 0, 2, 8, 8, 1, 4, 3, 1, 0, 6, 7, 7, 2, 4, 3, 1, 1, 3, 5, 2, 6, 3, 0, 2, 3, 1, 4, 0, 9, 4, 5, 1, 2, 2, 4, 8, 5, 3, 6, 0, 3, 6, 0, 2, 0, 9, 4, 6, 9, 5, 5, 6, 8, 7, 4, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

2,4

COMMENTS

Essentially the same digit sequence as A239798, A019863 and A019827. - R. J. Mathar, Jul 03 2014

The minimal polynomial of this constant is x^2 - 11*x - 1. - Joerg Arndt, Jan 01 2017

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.12.1 Phase transitions in Lattice Gas Models, p. 347.

LINKS

Table of n, a(n) for n=2..104.

Eric Weisstein's MathWorld, Hard Hexagon Entropy Constant

D. W. Wood and R. W. Turnbull, z^2-11z-1 as an algebraic invariant for the hard-hexagon model, 1988 J. Phys. A: Math. Gen. 21 L989.

Wikipedia, Hard Hexagon Model

FORMULA

((1 + sqrt(5))/2)^5 = (11 + 5*sqrt(5))/2.

EXAMPLE

11.09016994374947424102293417182819058860154589902881431067724311352630...

MATHEMATICA

RealDigits[GoldenRatio^5, 10, 103] // First

PROG

(PARI) (5*sqrt(5)+11)/2 \\ Charles R Greathouse IV, Aug 10 2016

CROSSREFS

Cf. A085850.

Sequence in context: A197070 A197333 A226120 * A277524 A118811 A200488

Adjacent sequences:  A244590 A244591 A244592 * A244594 A244595 A244596

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Jul 01 2014

STATUS

approved

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Last modified March 22 10:07 EDT 2019. Contains 321421 sequences. (Running on oeis4.)