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A286742 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.

%I A286742 #8 May 13 2017 23:46:03
%S A286742 7,24,628,1687,10793,376848,1530012,18660270,278567575,1695509434,
%T A286742 11136696004,102111268282,1260654956982,10725187563686,
%U A286742 308788493220130,4193528956200936,25999253094360135,118166387818704585,2161492060929047665,15963377896404315144
%N A286742 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 A286742 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 A286742 Table[
%t A286742    truncpi = Floor[10^(n - 1)*Pi]/10^(n - 1);
%t A286742     SortBy[
%t A286742       {Floor[1/(Pi - truncpi)], Ceiling[1/(Pi - truncpi)]},
%t A286742       N[Abs[Pi - (truncpi + 1/#)]] &
%t A286742    ][[1]],
%t A286742 {n, 1, 20}] (* first 20 terms *)
%Y A286742 Cf. A074783.
%K A286742 nonn,base
%O A286742 1,1
%A A286742 _Jason Zimba_, May 13 2017