OFFSET
1,1
COMMENTS
If there is a set of consecutive integers 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 A138336). [Sentence is not clear - N. J. A. Sloane, Dec 09 2017]
Comment from Joerg Arndt, Mar 17 2008: Does Mathematica's N[((quantity)), n] round a number (if so, to what base?) or truncate it? Is Mathematica's Recognize[] guaranteed to give the correct relation? I do not think so: that would be a major breakthrough. That is, this sequence may not even be well-defined.
This sequence is indeed ill defined. One can get the same approximation of Pi to a given precision with infinitely many distinct quadratic polynomials and any such polynomial that gives Pi to n+1 digits also gives Pi to n digits, so this sequence shouldn't have any term. Also, the 18-digit "root" given in the example isn't a root, the polynomial has a value of -5e-13 at this x-value. - M. F. Hasler, May 21 2025
EXAMPLE
a(1)=19 because 3.141592653589793238 (18 digits) is root of -3061495 + 674903*x + 95366*x^2 and 3.1415926535897932385 (19 digits) also is root of that same polynomial -3061495 + 674903*x + 95366*x^2.
MATHEMATICA
<< NumberTheory`Recognize`
b = {}; a = {};
Do[k = Recognize[N[Pi, n], 2, x]; If[MemberQ[a, k], AppendTo[b, n], AppendTo[a, k]], {n, 2, 300}]; b (* Artur Jasinski *)
CROSSREFS
KEYWORD
dead
AUTHOR
Artur Jasinski, Mar 15 2008
STATUS
approved