%I A138335
%S A138335 19,28,29,34,36,37,39,43,50,52,62,68,71,74,75,87,89,94,110,113,128,129,
%T A138335 130,132,137,143,153,169,174,189,201,203,207,209,211,217,240,241,242,
%U A138335 252,253,268,274,275,278,279,284,286,287,297
%N A138335 Positions of digits after decimal point of number Pi where the approximation 
               to the number Pi by a root of a polynomial of 2 degree does not improve 
               the accuracy.
%C A138335 If there is a set of consecutive numbers in this sequence starting at 
               k, this means that k-1 is a good approximation to Pi.
%C A138335 If the set of successive integers is longer that approximation k-1 better 
               (see A138336).
%C A138335 Comment from Joerg Arndt (arndt(AT)jjj.de), Mar 17 2008: Does Mathematica's 
               N[((quantity)), n] round a number (if so, to what base?) or truncate 
               it? Is Mathematica's Recognize[] guaranteed to give the correct relation? 
               I do not think so: that would be a major breakthrough. That is, this 
               sequence may not even be well-defined.
%e A138335 a(1)=19 because 3.141592653589793238 (18 digits) is root of -3061495+674903*x+95366*x^2 
               and 3.1415926535897932385 (19 digits) also is root of that same polynomial 
               -3061495+674903*x+95366*x^2
%t A138335 << NumberTheory`Recognize` b = {}; a = {}; Do[k = Recognize[N[Pi,n], 
               2, x]; If[MemberQ[a, k], AppendTo[b, n], AppendTo[a, k]], {n, 2, 
               300}]; b (*Artur Jasinski*)
%Y A138335 Sequence in context: A147232 A141417 A069529 this_sequence A091448 A067777 
               A065207
%Y A138335 Adjacent sequences: A138332 A138333 A138334 this_sequence A138336 A138337 
               A138338
%K A138335 nonn,base
%O A138335 1,1
%A A138335 Artur Jasinski (grafix(AT)csl.pl), Mar 15 2008