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A242565 Numbers k such that (k!+1)/(k+1) is prime. 1
4, 6, 10, 28, 772, 1320, 2620 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Subsequence of A006093.
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).
a(8) > 4725.
If it exists, a(8) > 6778. - J.W.L. (Jan) Eerland, Aug 15 2022
LINKS
EXAMPLE
(4!+1)/(4+1) = 5 is prime. Thus, 4 is a member of this sequence.
MATHEMATICA
ParallelTable[If[PrimeQ[(Factorial[n]+1)/(n+1)], n, Nothing], {n, 1, 5*10^3}]//.{}->Nothing (* J.W.L. (Jan) Eerland, Aug 15 2022 *)
PROG
(PARI) for(n=1, 5000, s=((prime(n)-1)!+1)/(prime(n)); if(ispseudoprime(s), print1(prime(n)-1)))
CROSSREFS
Cf. A006093.
Sequence in context: A252656 A322961 A291542 * A032392 A253048 A271956
KEYWORD
nonn,more,hard
AUTHOR
Derek Orr, May 17 2014
STATUS
approved

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Last modified July 23 03:10 EDT 2024. Contains 374544 sequences. (Running on oeis4.)