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%I #27 Jan 12 2024 22:21:47
%S 1,4,323,939,14341,61716,1621261,9192919,324707423,509838905,
%T 30546664503,59359795395,3329737379233,9164547454619
%N a(n) is the n-digit denominator of the fraction h/k with h and k coprime palindrome positive integers at which abs(h/k-e) is minimal.
%C a(3) = 323 corresponds to the denominator of A368617.
%H David A. Corneth, <a href="/A368618/a368618.gp.txt">PARI program</a>
%H <a href="/index/Ea">Index entries for sequences related to the number e</a>
%e n fraction approximated value
%e - ------------------- ------------------
%e 1 3/1 3
%e 2 11/4 2.75
%e 3 878/323 2.7182662538699...
%e 4 2552/939 2.7177848775292...
%e 5 38983/14341 2.7182902168607...
%e 6 167761/61716 2.7182740294251...
%e 7 4407044/1621261 2.7182816338640...
%e 8 24988942/9192919 2.7182815382143...
%e 9 882646288/324707423 2.7182818299783...
%e ...
%t a[1]=1; a[n_]:=Module[{minim = Infinity}, h = Select[Range[10^(n - 1), 10^n - 1], PalindromeQ]; lh = Length[h]; For[i = 1, i <= lh, i++, k = Select[Range[Floor[Part[h, i]/E], Ceiling[Part[h, i]/E]], PalindromeQ]; lk = Length[k]; For[j = 1, j <= lk, j++, If[(dist = Abs[Part[h, i]/Part[k, j] - E]) < minim && GCD[Part[h, i], Part[k, j]] == 1, minim = dist; kmin = Part[k, j]]]]; kmin]; Array[a,9]
%o (PARI) \\ See PARI program in Links
%Y Cf. A001113, A002113, A070252, A368617, A368618 (numerator), A368658.
%Y Cf. A007676, A007677.
%Y Cf. A364845 (similar for Pi), A368620, A368621.
%K nonn,base,frac,more
%O 1,2
%A _Stefano Spezia_, Jan 01 2024
%E a(10)-a(14) from _David A. Corneth_, Jan 03 2024