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%I #14 Aug 12 2023 00:54:30
%S 3,22,474,1551,36163,292292,7327237,31311313
%N a(n) is the n-digit numerator of the fraction h/k with h and k coprime palindrome positive integers at which abs(h/k-Pi) is minimal.
%C a(2) = 22 corresponds to the numerator of A068028.
%H <a href="/index/Ph#Pi314">Index entries for sequences related to the number Pi</a>
%e n fraction approximated value
%e - ------------------- ------------------
%e 1 3 3
%e 2 22/7 3.1428571428571...
%e 3 474/151 3.1390728476821...
%e 4 1551/494 3.1396761133603...
%e 5 36163/11511 3.1416036834332...
%e 6 292292/93039 3.1416072829673...
%e 7 7327237/2332332 3.1415926206046...
%e 8 31311313/9966699 3.1415931192464...
%e ...
%t nmax = 8; a = {3}; hmin = kmin = 0; For[n = 2, n <= nmax, n++, minim = Infinity; h = Select[Range[10^(n - 1), 10^n - 1], PalindromeQ]; k = Select[Range[10^(n - 2), 10^n - 1], PalindromeQ]; lh = Length[h]; lk = Length[k]; For[i = 1, i <= lh, i++, For[j = 1, j <= lk, j++, If[(dist = Abs[Part[h, i]/Part[k, j] - Pi]) < minim && GCD[Part[h, i], Part[k, j]] == 1, minim = dist; hmin = Part[h, i]]]]; AppendTo[a, hmin]]; a
%Y Cf. A000796, A002113, A068028, A070252, A364845 (denominator), A364846.
%Y Cf. A355622, A355623.
%K nonn,base,frac,more
%O 1,1
%A _Stefano Spezia_, Aug 10 2023
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