This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A362006 #17 Apr 22 2023 21:48:04
%S A362006 0,1,4,8,9,12,15,17,19,24,25,29,30,34,37,39,41,44,48,49,52,55,59,61,
%T A362006 62,66,68,70,74,79,79,82,84,89,89,92,96,98,102,103,106,110,112,114,
%U A362006 116,122,124,126,128,132,133,137,138,141,144,147,151,152,154,158,161
%N A362006 a(n) is the minimum integer m such that floor(e^n) = floor(Sum_{k=0..m} (n^k)/(k!)).
%C A362006 Conjecture: a(n) ~ e*n as n->infinity.
%C A362006 Conjecture: a(n) <= 3n for all n.
%C A362006 The second one would imply: A000149(n) = floor(Sum_{k=0..3n} (n^k)/(k!)).
%e A362006 a(3) = 8 since floor(e^3) = 20, floor(Sum_{k=0..8} (n^k)/(k!)) = 20 and "8" is the minimum because floor(Sum_{k=0..7} (n^k)/(k!)) = 19.
%t A362006 f[n_, m_] := Floor[Sum[(n^k)/(k!), {k, 0, m}]] - Floor[E^n];
%t A362006 a[n_] := Min[Flatten[Position[Table[f[n, m], {m, 0, 150}], 0]]] - 1;
%t A362006 Table[a[n], {n, 1, 50}]
%o A362006 (PARI) a(n) = my(m=0, x=floor(exp(n)), y=1); while(floor(y) != x, m++; y += n^m/m!); m; \\ _Michel Marcus_, Apr 14 2023
%Y A362006 Cf. A000149.
%K A362006 nonn
%O A362006 0,3
%A A362006 _Luca Onnis_, Apr 03 2023