cp's OEIS Frontend

A355623 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.

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