A086311 - OEIS

%I #14 Jul 30 2015 22:04:50

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

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.14 Digital Search Tree Constants, p. 356.

%H Vincenzo Librandi, <a href="/A086311/b086311.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TreeSearching.html">Tree Searching</a>

%F 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 2.84438316811675616821622572314100826648903853090871...

%t 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 Cf. A086312.

%K nonn,cons

%O 1,1

%A _Eric W. Weisstein_, Jul 15 2003