%I #8 May 13 2017 23:46:03
%S 7,24,628,1687,10793,376848,1530012,18660270,278567575,1695509434,
%T 11136696004,102111268282,1260654956982,10725187563686,
%U 308788493220130,4193528956200936,25999253094360135,118166387818704585,2161492060929047665,15963377896404315144
%N a(n) minimizes (over the integers) the absolute difference between Pi and x(n) + 1/a(n), where x(n) is Pi truncated at the n-th decimal digit.
%e 3 + 1/7 is closest to Pi in absolute value among numbers of the form 3 + 1/k (k an integer); 3.1 + 1/24 is closest to Pi in absolute value among numbers of the form 3.1 + 1/k (k an integer); 3.14 + 1/628 is closest to Pi in absolute value among numbers of the form 3.14 + 1/k (k an integer).
%t Table[
%t truncpi = Floor[10^(n - 1)*Pi]/10^(n - 1);
%t SortBy[
%t {Floor[1/(Pi - truncpi)], Ceiling[1/(Pi - truncpi)]},
%t N[Abs[Pi - (truncpi + 1/#)]] &
%t ][[1]],
%t {n, 1, 20}] (* first 20 terms *)
%Y Cf. A074783.
%K nonn,base
%O 1,1
%A _Jason Zimba_, May 13 2017