cp's OEIS Frontend

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.

%I A138337 #10 May 27 2025 16:00:18
%S A138337 7,13,17,30,37,48,62,63,77,81,86,92,97,114,117,125,129,143,148,152,
%T A138337 156,159,168,174,180,185,196,200,204,211,227,235,244,247,259,266,267,
%U A138337 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)
%C A138337 This sequence appears to be ill defined: There are many different polynomials of degree 3 that give an approximation of Pi with the same precision, and any such approximation to n+1 digits is also an approximation of Pi to n digits, so the sequence should be empty. - _M. F. Hasler_, May 21 2025
%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
%Y A138337 Cf. A138335, A138336, A138338.
%K A138337 dead
%O A138337 1,1
%A A138337 _Artur Jasinski_, Mar 15 2008