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 A092984 #19 Jul 14 2025 16:16:29
%S A092984 1,1,1,2,2,1,2,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,
%T A092984 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A092984 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A092984 a(n) = the least k >= 1 such that n! + k is squarefree.
%C A092984 Conjecture: There exists a finite k such that a(n) < k for all n. Subsidiary sequence: Index of the first occurrence of n in this sequence. In case the conjecture is true, this sequence would be finite.
%C A092984 If a(n) = 2 ==> n!+1 is divisible by a square (sequence A064237). - Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 29 2004
%F A092984 a(n) = A092983(n) - n!.
%e A092984 a(5) = 2 = 122 - 5! = 122 - 120 (as 121 = 11^2 is not squarefree).
%t A092984 Table[SelectFirst[Range@ 10, SquareFreeQ[n! + #] &], {n, 45}] (* _Michael De Vlieger_, Aug 23 2017 *)
%t A092984 Table[Module[{k=1,c=n!},While[!SquareFreeQ[c+k],k++];k],{n,110}] (* _Harvey P. Dale_, Jul 14 2025 *)
%o A092984 (PARI) a(n)=for(i=1,n!,if(issquarefree(n!+i),return(i)))
%o A092984 (PARI) A092984(n) = { my(k=1); while(!issquarefree(n!+k), k++); k; }; \\ _Antti Karttunen_, Aug 22 2017
%Y A092984 Cf. A000142, A064237, A092983.
%K A092984 nonn
%O A092984 1,4
%A A092984 _Amarnath Murthy_, Mar 28 2004
%E A092984 More terms from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 29 2004
%E A092984 More terms from _David Wasserman_, Sep 27 2006
%E A092984 Typo in description corrected by _Antti Karttunen_, Aug 22 2017