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.
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(4) = 7, because 4! + 7^2 = 73 is prime and for 0 < i < 7, 4! + i^2 is not prime.
Table[SelectFirst[Range@ 10000, PrimeQ[n! + #^2] &], {n, 120}]
(* Version 10, or *)
Table[k = 1; While[! PrimeQ[n! + k^2], k++]; k, {n, 120}] (* Michael De Vlieger, Feb 28 2016 *)
a(n) = {my(k=1); while (!isprime(n! + k^2), k++); k;} \\ Michel Marcus, Feb 29 2016
3 is a term because 2*3 + 1 = 7 is prime. 4 is a term because 1*3*4 + 1 = 13 is prime. 5 is a term because 1*2*4*5 + 1 = 41 is prime. 6 is a term because 1*2*3*5*6 + 1 = 181 is prime. 7 is a term because 1*2*3*4*6*7 + 1 = 1009 is prime.
[n: n in [3..500] | IsPrime(Factorial(n) div (n-2) + 1)]; // Vincenzo Librandi, Apr 07 2016
Select[Range[3, 2000], PrimeQ[( #! / (# - 2) + 1)] &] (* Vincenzo Librandi, Apr 07 2016 *)
lista(nn) = for(n=3, nn, if(ispseudoprime(n!/(n-2)+1), print1(n, ", ")));
ABC2 $a!/($a-2) + 1 a: from 3 to 100000
Do[If[PrimeQ[FromDigits[Reverse[IntegerDigits[n! + 1]]]], Print[n]], {n, 400}] (* Vincenzo Librandi, Jan 25 2018 *)
isok(n) = isprime(fromdigits(Vecrev(digits(n!+1)))); \\ Michel Marcus, Jan 26 2018
select(k -> isprime((2*k+1)*k!+1), [$0 .. 300])[];
Do[If[PrimeQ[(2*k + 1)*Factorial[k] + 1], Print[k]], {k, 0, 3000}]
for(k=0, 3000, if(isprime((2*k+1)*k!+1), print1(k", ")))
for k in range(3000):
if is_prime((2*k+1)*factorial(k) + 1):
print(k)
a(5)=241 because in arithmetic progression 120k+1=5!k+1 the second term is prime, 241.
sp[n_]:=Module[{nf=n!,k=1},While[!PrimeQ[nf*k+1],k++];nf*k+1]; Array[sp,20] (* Harvey P. Dale, Jan 27 2013 *)
a(n) = for(k=1, oo, if(isprime(k*n! + 1), return(k*n! + 1))); \\ Daniel Suteu, Oct 18 2020
isok(n) = isprime((n!)^2-n!+1); \\ Michel Marcus, Aug 26 2013
5 is in the sequence because (5!)^2 + 5! - 1 = 14519 is prime.
Do[If[PrimeQ[n!^2+n!-1], Print[n]], {n, 600}]
7 is in the sequence because 7^7*7! + 1 = 4150656721 is prime.
Do[If[PrimeQ[n^n*n!+1], Print[n]], {n, 600}]
4 is in the sequence because 8! - 6! + 4! - 2! + 1 = 39623 is prime.
Do[If[PrimeQ[Sum[(-1)^(n-k)(2k)!, {k, 0, n}]], Print[n]], {n, 1000}]
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