1,1

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

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

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

Cf. A138335, A138336, A138338.

Sequence in context: A154408 A089531 A247010 * A359063 A174877 A230433

Adjacent sequences: A138334 A138335 A138336 * A138338 A138339 A138340

Artur Jasinski, Mar 15 2008

approved