OFFSET
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.13 Binary search tree constants, p. 356.
LINKS
Eric Weisstein's World of Mathematics, Tree Searching
FORMULA
EXAMPLE
0.37204...
MATHEMATICA
digits = 102; m0 = 100; dm = 100; Clear[theta]; theta[m_] := theta[m] = Sum[((k*2^(k*((k-1)/2)))*Sum[1/(2^j-1), {j, 1, k}])/Product[2^j-1, {j, 1, k}], {k, 1, m}] // N[#, digits+10]&; theta[m0]; theta[m = m0+dm]; While[RealDigits[theta[m], 10, digits+10] != RealDigits[theta[m-dm], 10, digits+10], m = m+dm]; theta0 = theta[m]; Clear[Q]; Q[m_] := Q[m] = Product[1-1/2^k, {k, 1, m}] // N[#, digits+10]&; Q[m0]; Q[m = m0+dm]; While[RealDigits[Q[m], 10, digits+10] != RealDigits[Q[m-dm], 10, digits+10], m = m+dm]; Q0 = Q[m]; Clear[alpha]; alpha[m_] := alpha[m] = Sum[1/(2^k-1), {k, 1, m}] // N[#, digits+10]&; alpha[m0]; alpha[m = m0+dm]; While[RealDigits[alpha[m], 10, digits+10] != RealDigits[alpha[m-dm], 10, digits+10], m = m+dm]; alpha0 = alpha[m]; c = theta0+1-1/Q0*(1/Log[2]+alpha0^2-alpha0); RealDigits[c, 10, digits] // First (* Jean-François Alcover, Jun 27 2014 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Jul 15 2003
STATUS
approved