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A138335
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Positions of digits after decimal point of number Pi where the approximation to the number Pi by a root of a polynomial of 2 degree does not improve the accuracy.
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12
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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 A138336).
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.
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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
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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*)
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CROSSREFS
| Sequence in context: A147232 A141417 A069529 * A173639 A091448 A067777
Adjacent sequences: A138332 A138333 A138334 * A138336 A138337 A138338
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KEYWORD
| nonn,base
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Mar 15 2008
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