A242743 - OEIS

A242743

Decimal expansion of an Ising constant related to the random coloring problem.

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

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OFFSET

0,1

COMMENTS

In Ising model on the 2D square lattice, the negated ratio of free energy per node to the temperature at the critical point. - Andrey Zabolotskiy, Sep 12 2017

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.22 Lenz-Ising constants, p. 399.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

Lars Onsager, Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition, Phys. Rev. 65, 117 (1944) [see eq. (121)].

FORMULA

log(2)/2 + 2*G/Pi = log(2)/2 + A218387/2, where G is Catalan's constant.

EXAMPLE

0.929695398341610214985384973665878...

MATHEMATICA

RealDigits[Log[2]/2 + 2*Catalan/Pi, 10, 105] // First

PROG

(PARI) default(realprecision, 100); log(2)/2 + 2*Catalan/Pi \\ G. C. Greubel, Aug 25 2018

(Magma) SetDefaultRealField(RealField(100)); R:=RealField(); Log(2)/2 + 2*Catalan(R)/Pi(R); // G. C. Greubel, Aug 25 2018

CROSSREFS

Cf. A002898, A006752, A218387, A245592.

Sequence in context: A230157 A260646 A200234 * A197812 A146492 A266565

Adjacent sequences: A242740 A242741 A242742 * A242744 A242745 A242746

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Jun 02 2014

STATUS

approved