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%I #46 Sep 06 2022 10:28:59
%S 1,29,185,1745,16825,317899,2474777,29803639,134433224,2925310919,
%T 14459352454,150413935274,1841255744875,15715280017394,
%U 298973571352939,2949399321185629,16854427454794925,303090351024681259,3130972820121426389,11582111864577268363,140797308252987723244
%N 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.
%C a(n) and R(a(n)) have the same number of digits.
%C 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.
%D Petr Beckmann, A History of Pi, 3rd Ed., Boulder, Colorado: The Golem Press (1974): p. 27.
%H Bert Dobbelaere, <a href="/A355623/b355623.txt">Table of n, a(n) for n = 1..22</a>
%e n fraction approximated value
%e - ------------------- ------------------
%e 1 1 1
%e 2 92/29 3.1724137931034...
%e 3 581/185 3.1405405405405...
%e 4 5471/1745 3.1352435530086...
%e 5 52861/16825 3.1418127786033...
%e 6 998713/317899 3.1416047235128...
%e 7 7774742/2474777 3.1415929596889...
%e 8 93630892/29803639 3.1415926088757...
%e 9 422334431/134433224 3.1415926690860...
%e ...
%t 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
%Y Cf. A000796, A002485, A004086, A067251.
%Y Cf. A355622 (numerator or digital reversal).
%K nonn,base,frac
%O 1,2
%A _Stefano Spezia_, Jul 10 2022
%E a(10)-a(19) from _Bert Dobbelaere_, Jul 17 2022
%E a(20)-a(21) from _Bert Dobbelaere_, Sep 05 2022
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