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Search: id:A138337
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| A138337 |
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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 3 degree does not improve the accuracy. |
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+0
12
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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)
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EXAMPLE
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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
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MATHEMATICA
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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 (*Artur Jasinski*)
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CROSSREFS
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Cf. A138335, A138336, A138338.
Sequence in context: A154408 A154411 A089531 this_sequence A029477 A019378 A005762
Adjacent sequences: A138334 A138335 A138336 this_sequence A138338 A138339 A138340
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KEYWORD
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nonn,uned,probation,base
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Mar 15 2008
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