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A355623
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a(n) is the n-digit positive number with no trailing zeros and coprime to its digital reversal R(a(n)) at which abs(R(a(n))/a(n)-Pi) is minimized.
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5
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1, 29, 185, 1745, 16825, 317899, 2474777, 29803639, 134433224, 2925310919, 14459352454, 150413935274, 1841255744875, 15715280017394, 298973571352939, 2949399321185629, 16854427454794925, 303090351024681259, 3130972820121426389, 11582111864577268363, 140797308252987723244
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OFFSET
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1,2
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COMMENTS
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a(n) and R(a(n)) have the same number of digits.
Petr Beckmann wrote that the fraction 92/29, corresponding to the second term of the sequence, appeared as value of Pi in a document written in A.D. 718.
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REFERENCES
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Petr Beckmann, A History of Pi, 3rd Ed., Boulder, Colorado: The Golem Press (1974): p. 27.
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LINKS
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EXAMPLE
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n fraction approximated value
- ------------------- ------------------
1 1 1
2 92/29 3.1724137931034...
3 581/185 3.1405405405405...
4 5471/1745 3.1352435530086...
5 52861/16825 3.1418127786033...
6 998713/317899 3.1416047235128...
7 7774742/2474777 3.1415929596889...
8 93630892/29803639 3.1415926088757...
9 422334431/134433224 3.1415926690860...
...
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MATHEMATICA
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nmax=9; a={}; For[n=1, n<=nmax, n++, minim=Infinity; For[k=10^(n-1), k<=10^n-1, k++, If[(dist=Abs[FromDigits[Reverse[IntegerDigits[k]]]/k-Pi]) < minim && Last[IntegerDigits[k]]!=0 && GCD[k, FromDigits[Reverse[IntegerDigits[k]]]]==1, minim=dist; kmin=k]]; AppendTo[a, kmin]]; a
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CROSSREFS
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Cf. A355622 (numerator or digital reversal).
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KEYWORD
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nonn,base,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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