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.

7, 13, 17, 30, 37, 48, 62, 63, 77, 81, 86, 92, 97, 114, 117, 125, 129, 143, 148, 152, 156, 159, 168, 174, 180, 185, 196, 200, 204, 211, 227, 235, 244, 247, 259, 266, 267, 282

Offset: 1

Author

Artur Jasinski, Mar 15 2008

Keywords

• dead

Comments

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.

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

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

Examples

			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
		

Crossrefs

Cf. A138335, A138336, A138338.

Programs

Mathematica

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