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A086311 Decimal expansion of constant appearing in the variance for searching in a digital tree.

%I A086311 #15 Feb 16 2025 08:32:50
%S A086311 2,8,4,4,3,8,3,1,6,8,1,1,6,7,5,6,1,6,8,2,1,6,2,2,5,7,2,3,1,4,1,0,0,8,
%T A086311 2,6,6,4,8,9,0,3,8,5,3,0,9,0,8,7,1,0,7,7,4,3,9,5,5,3,7,5,4,6,6,6,3,6,
%U A086311 8,1,9,0,2,3,9,4,2,4,1,2,7,7,7,4,8,8,2,1,9,5,7,9,1,7,1,8,4,8,8,0,2,5
%N A086311 Decimal expansion of constant appearing in the variance for searching in a digital tree.
%D A086311 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.14 Digital Search Tree Constants, p. 356.
%H A086311 Vincenzo Librandi, <a href="/A086311/b086311.txt">Table of n, a(n) for n = 1..1000</a>
%H A086311 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TreeSearching.html">Tree Searching</a>
%F A086311 1/12 + (Pi^2+6)/(6*log(2)^2) - alpha - beta, where gamma is Euler's constant, alpha is the Erdős-Borwein constant (A065442) and beta is A065443. - _Jean-François Alcover_, Jul 29 2014, after Steven Finch
%e A086311 2.84438316811675616821622572314100826648903853090871...
%t A086311 digits = 102; alpha =  NSum[1/(2^k-1), {k, 1, 500}, NSumTerms -> 100, WorkingPrecision -> digits+10]; beta = NSum[1/(2^k-1)^2, {k, 1, 500}, NSumTerms -> 100, WorkingPrecision -> digits+10]; RealDigits[1/12 + (Pi^2+6)/(6*Log[2]^2) - alpha - beta, 10, digits] // First
%Y A086311 Cf. A086312.
%K A086311 nonn,cons
%O A086311 1,1
%A A086311 _Eric W. Weisstein_, Jul 15 2003