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 A242565 Numbers k such that (k!+1)/(k+1) is prime. 1

%I #21 Sep 13 2022 08:33:44

%S 4,6,10,28,772,1320,2620

%N Numbers k such that (k!+1)/(k+1) is prime.

%C Subsequence of A006093.

%C It is unknown whether this sequence is infinite. If S = (n!+k)/(n+k), when k > 1, there are finitely many n-values that make S an integer. When k = 1, there are infinitely many n-values that make S an integer (A006093).

%C a(8) > 4725.

%C If it exists, a(8) > 6778. - _J.W.L. (Jan) Eerland_, Aug 15 2022

%e (4!+1)/(4+1) = 5 is prime. Thus, 4 is a member of this sequence.

%t ParallelTable[If[PrimeQ[(Factorial[n]+1)/(n+1)],n,Nothing],{n,1,5*10^3}]//.{}->Nothing (* _J.W.L. (Jan) Eerland_, Aug 15 2022 *)

%o (PARI) for(n=1,5000,s=((prime(n)-1)!+1)/(prime(n)); if(ispseudoprime(s), print1(prime(n)-1)))

%Y Cf. A006093.

%K nonn,more,hard

%O 1,1

%A _Derek Orr_, May 17 2014

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Last modified August 11 17:54 EDT 2024. Contains 375073 sequences. (Running on oeis4.)