cp's OEIS Frontend

A086312 Decimal expansion of constant appearing in the variance for inserting in a digital tree.

%I A086312 #15 Feb 16 2025 08:32:50
%S A086312 7,6,3,0,1,4,1,8,7,1,1,1,1,4,8,3,7,0,3,4,6,6,4,4,1,1,9,4,0,6,0,1,6,8,
%T A086312 4,1,4,2,4,9,9,1,3,7,5,2,6,2,6,2,9,7,4,2,7,6,8,9,7,9,1,0,9,0,1,7,5,7,
%U A086312 3,2,1,9,9,9,3,1,7,7,2,1,0,0,0,7,6,2,0,2,0,8,1,1,1,2,8,7,2,3,4,5,8,3
%N A086312 Decimal expansion of constant appearing in the variance for inserting in a digital tree.
%D A086312 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.14 Digital Search Tree Constants, p. 356.
%H A086312 Vincenzo Librandi, <a href="/A086312/b086312.txt">Table of n, a(n) for n = 0..1000</a>
%H A086312 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TreeSearching.html">Tree Searching</a>
%F A086312 1/12 + Pi^2/(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 A086312 0.76301418711114837034664411940601684142499137526...
%t A086312 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*Log[2]^2) - alpha - beta, 10, digits] // First
%Y A086312 Cf. A086311.
%K A086312 nonn,cons
%O A086312 0,1
%A A086312 _Eric W. Weisstein_, Jul 15 2003