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A246847
Decimal expansion of beta_0, a threshold constant [the existence or not of a giant component] associated with random graph theory in case of a power law distribution for the degree sequence.
0
3, 4, 7, 8, 7, 5, 0, 7, 8, 5, 7, 3, 3, 9, 6, 0, 2, 6, 0, 6, 7, 1, 4, 8, 7, 2, 6, 1, 3, 9, 0, 3, 3, 5, 4, 0, 4, 3, 4, 3, 1, 2, 6, 3, 0, 2, 5, 7, 2, 5, 9, 8, 8, 5, 8, 6, 2, 4, 2, 0, 6, 6, 5, 5, 5, 9, 2, 0, 6, 6, 4, 6, 5, 8, 7, 3, 0, 3, 7, 9, 3, 3, 4, 0, 9, 8, 0, 8, 5, 3, 8, 0, 8, 8, 5, 8, 7, 4, 5, 1, 8, 2, 5, 4
OFFSET
1,1
LINKS
W. Aiello, F. Chung, L. Lu, A random graph model for power law graphs, Experiment. Math. Volume 10, Issue 1 (2001), 53-66.
M. E. J. Newman, The structure and function of complex networks, arXiv:cond-mat/0303516 [cond-mat.stat-mech], 2003, page 24.
FORMULA
Solution of zeta(beta - 2) - 2*zeta(beta - 1) = 0, beta > 3.
EXAMPLE
3.4787507857339602606714872613903354043431263025725988586242...
MATHEMATICA
beta0 = beta /. FindRoot[Zeta[beta - 2] - 2*Zeta[beta - 1] == 0, {beta, 7/2}, WorkingPrecision -> 104]; RealDigits[beta0] // First
PROG
(PARI) solve(x=3.4, 4, zeta(x-2)-2*zeta(x-1)) \\ Charles R Greathouse IV, Sep 09 2014
CROSSREFS
Sequence in context: A056007 A316973 A213622 * A193406 A104426 A097044
KEYWORD
nonn,cons
AUTHOR
STATUS
approved