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.
Select[Range[80],With[{c=#!},AllTrue[c^2+{c+1,1},PrimeQ]]&] (* Harvey P. Dale, Aug 11 2025 *)
3 is in the sequence because Phi(7,3!) = 1 + 6 + 6^2 + 6^3 + 6^4 + 6^5 + 6^6 = 55987 is prime.
Select[Range[0, 6502], PrimeQ[Cyclotomic[7, #!]] &]
a:= n-> max(numtheory[factorset](n!^2+1)): seq(a(n), n=0..20); # Alois P. Heinz, Mar 19 2018
a(n) = vecmax(factor(n!^2 + 1)[,1]); \\ Daniel Suteu, Jun 10 2022
a(0)=0 because (0!)^2 + 0 + 0 + 1 = 2 is prime. a(1)=0 because (1!)^2 + 1 + 0 + 1 = 3 is prime. a(2)=0 because (2!)^2 + 2 + 0 + 1 = 7 is prime. a(3)=1 because (3!)^2 + 3 + 1 + 1 = 41 is prime and 40 is not prime. a(4)=6 because (4!)^2 + 4 + 6 + 1 = 587 is prime and 581, 582, ... , 586 are not prime.
a(n) = apply(x->(nextprime(x)-x), (n!)^2+n+1); \\ Altug Alkan, Mar 21 2018
isok(n) = isprime((n!)^2-n!+1); \\ Michel Marcus, Aug 26 2013
Do[f=(n!)^8+1;If[PrimeQ[f],Print[{n,f}]],{n,1,75}]
a(7) = 14 because (14!)^3+(14!)^2+1 = 662559760556747835222526525440001 is prime.
[n: n in [0..160]|IsPrime((Factorial(n)^3)+(Factorial(n)^2)+1)]; // Vincenzo Librandi, Dec 22 2010
Select[Range[200], PrimeQ[#!^3 + #!^2 + 1] &]
2 is in the sequence because Phi(9,2!) = 1 + 2^3 + 2^6 = 73 is prime.
Select[Range[0, 5944], PrimeQ[Cyclotomic[9, #!]] &]
2 is in the sequence because Phi(10,2!) = 1 - 2 + 2^2 - 2^3 + 2^4 = 11 is prime.
Select[Range[0, 7560], PrimeQ[Cyclotomic[10, #!]] &]
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