A138337 - OEIS

%I #6 Jan 20 2022 12:52:56

%S 7,13,17,30,37,48,62,63,77,81,86,92,97,114,117,125,129,143,148,152,

%T 156,159,168,174,180,185,196,200,204,211,227,235,244,247,259,266,267,

%U 282

%N 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 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 If the set of successive integers is longer that approximation k-1 better (see A138338)

%e 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 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

%Y Cf. A138335, A138336, A138338.

%K nonn,uned,base

%O 1,1

%A _Artur Jasinski_, Mar 15 2008