

A138335


Positions of digits after decimal point in decimal expansion of Pi where the approximation to Pi by a root of a quadratic polynomial does not improve the accuracy.


12



19, 28, 29, 34, 36, 37, 39, 43, 50, 52, 62, 68, 71, 74, 75, 87, 89, 94, 110, 113, 128, 129, 130, 132, 137, 143, 153, 169, 174, 189, 201, 203, 207, 209, 211, 217, 240, 241, 242, 252, 253, 268, 274, 275, 278, 279, 284, 286, 287, 297
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OFFSET

1,1


COMMENTS

If there is a set of consecutive integers in this sequence starting at k, this means that k1 is a good approximation to Pi.
If the set of successive integers is longer that approximation k1 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 welldefined.


LINKS

Table of n, a(n) for n=1..50.


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

Sequence in context: A141417 A264834 A069529 * A304367 A298638 A291884
Adjacent sequences: A138332 A138333 A138334 * A138336 A138337 A138338


KEYWORD

nonn,base,less


AUTHOR

Artur Jasinski, Mar 15 2008


STATUS

approved



