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%I #18 Oct 18 2021 08:27:43
%S 4,5,6,7,9,9,10,11,12,13,14,16,16,16,17,18,19,20,20,22,22,22,23,24,24,
%T 26,26,27,28,28,29,30,30,31,31,32,33,33,34,35,35,36,36,37,38,38,39,40,
%U 40,41,42,42,43,43,44,45,45,46,46,47,48,48,49,50,50
%N Least m such that the first n digits (after the decimal point) of e and Sum_{k=0..m} 1/k! are the same.
%t a[n_] := Module[{e = Floor[10^n*E], s = 0, k = 0}, While[Floor[10^n*s] != e, s += 1/k!; k++]; k - 1]; Array[a, 65] (* _Amiram Eldar_, Sep 20 2021 *)
%Y Cf. A001113.
%K nonn,base
%O 1,1
%A _Angad Singh_, Sep 20 2021