%I A138337
%S A138337 7,13,17,30,37,48,62,63,77,81,86,92,97,114,117,125,129,143,148,152,156,
%T A138337 159,168,174,180,185,196,200,204,211,227,235,244,247,259,266,267,282
%N A138337 Positions of digits after decimal point of number Pi where the approximation 
               to the number Pi by a root of a polynomial of 3 degree does not improve 
               the accuracy.
%C A138337 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 A138337 If the set of successive integers is longer that approximation k-1 better 
               (see A138338)
%e A138337 a(1)=7 because 3.141593 (6 digits) is root of cubic 2 + 29 x - 22 x^2 
               + 4 x^3 and 3.1415927 (7 digits) also is root of that same polynomial 
               -3061495+674903*x+95366*x^2
%t A138337 b = {}; a = {}; Do[k = Recognize[N[Pi,n + 1], 3, x]; If[MemberQ[a, k], 
               AppendTo[b, n], AppendTo[a, k]], {n, 2, 300}]; b (*Artur Jasinski*)
%Y A138337 Cf. A138335, A138336, A138338.
%Y A138337 Sequence in context: A154408 A154411 A089531 this_sequence A029477 A019378 
               A005762
%Y A138337 Adjacent sequences: A138334 A138335 A138336 this_sequence A138338 A138339 
               A138340
%K A138337 nonn,uned,probation,base
%O A138337 1,1
%A A138337 Artur Jasinski (grafix(AT)csl.pl), Mar 15 2008