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.
f:= proc(n) local t,r,m;
r:= 1; t:= 1;
for m from 1 do
r:= r*m mod n;
if r = 0 then return 0 fi;
t:= t + r mod n;
if t = 0 then return m+1 fi;
od;
end proc:
f(1):= 1:
map(f, [$1..100]); # Robert Israel, Nov 14 2016
a[n_] := Module[{t, r, m}, r = 1; t = 1; For[m = 1, True, m++, r = Mod[r*m, n]; If[r == 0, Return[0]]; t = Mod[t+r, n]; If[t == 0, Return[m+1]]]];
Array[a, 100] (* Jean-François Alcover, Apr 12 2019, after Robert Israel *)
3 is in the sequence because A003422(1)=1 and A003422(2)=2 are not divisible by 3, and A003422(k) == 1 (mod 3) for k >= 3. 4 is not in the sequence because A003422(3) = 4 is divisible by 4.
filter:= proc(n) local t,r,m;
r:= 1; t:= 1;
for m from 1 do
r:= r*m mod n;
if r = 0 then return true fi;
t:= t + r mod n;
if t = 0 then return false fi;
od;
end proc:
select(filter, [$2..100]);
okQ[n_] := Module[{t, r, m}, r = 1; t = 1; For[m = 1, True, m++, r = Mod[r*m, n]; If[r == 0, Return[True]]; t = Mod[t + r, n]; If[t == 0, Return[False]]]];
Select[Range[2, 100], okQ] (* Jean-François Alcover, Apr 12 2019, after Robert Israel *)
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