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Search: id:A138343
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| A138343 |
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Positions of digits after decimal point of number Pi where the approximation to the number Pi by rational fraction does not improve the accuracy. |
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+0
10
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| 3, 5, 6, 7, 8, 12, 14, 21, 22, 23, 26, 29, 30, 35, 37, 38, 39, 45, 47, 49, 51, 55, 58, 59, 61, 63, 67, 69, 74, 77, 79, 80, 81, 82, 84, 85, 87, 88, 94, 95, 98, 101, 105, 108, 110, 113, 114, 116, 118, 121, 122, 125, 130, 133, 135, 139, 140, 141, 143, 145, 147, 148, 151
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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355/113 is good approximation for Pi because 4 successive integers occured in this sequence 5, 6, 7, 8
If the set of successive integers is longer that approximation k-1 better.
For smallest last integer after which occured exactly n successive integers see A138339
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EXAMPLE
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a(1)=3 because 3.14 (2 digits) is approximated by 22/7 and 3.1415 (rounded to 3 digits =3.142) also by 22/7
a(2)=5 because 3.14159 (rounded to 4 digits = 3.1416) is approximated by 355/113
and 3.14159 also bu 355/113 a(3)=6 and 3.1415926 (rounded to 5 digits 3.141593)
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MATHEMATICA
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<< NumberTheory`Recognize` b = {}; a = {}; Do[k = Recognize[N[Pi, n + 1], 1, x]; If[MemberQ[a, k], AppendTo[b, n], AppendTo[a, k]], {n, 1, 1000}]; b (*Artur Jasinski*)
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CROSSREFS
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Cf. A138335, A138336, A138337, A138338, A138339.
Adjacent sequences: A138340 A138341 A138342 this_sequence A138344 A138345 A138346
Sequence in context: A076054 A139636 A047583 this_sequence A010906 A114309 A079581
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KEYWORD
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nonn,uned,probation
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Mar 16 2008
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