A301423 - OEIS

%I #19 Jan 15 2023 02:07:59

%S 4,5,6,11,15,44,66,168,575,1713

%N Numbers k such that !k/(k-1) is prime, where !k = A000166(k) is the subfactorial of k.

%C Also numbers k such that A000255(k-2) is prime.

%C The corresponding primes are 3, 11, 53, 1468457, 34361893981, 22742406079421034331584846001936724930824184898296683, ...

%C a(11) > 35000. - _Robert Price_, Apr 14 2018

%t Select[Range[2,100], PrimeQ[Subfactorial[#]/(#-1)] &]

%o (PARI) isok(n) = (n != 1) && isprime(n!*sum(k=0, n, (-1)^k/k!)/(n-1)); \\ _Michel Marcus_, Mar 24 2018

%Y Cf. A000166, A000255.

%K nonn,more

%O 1,1

%A _Amiram Eldar_, Mar 20 2018