

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
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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^211z1 as an algebraic invariant for the hardhexagon 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 * A335415 A277524 A118811
Adjacent sequences: A244590 A244591 A244592 * A244594 A244595 A244596


KEYWORD

nonn,cons,easy


AUTHOR

JeanFrançois Alcover, Jul 01 2014


STATUS

approved



