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URL: https://oeis.org/A237443

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A237443
Numbers m such that (2m)! - m! + 1 is prime.
7
1, 2, 7, 13, 23, 5666, 32918
OFFSET
1,2
COMMENTS
If it exists, a(7) > 7*10^3. - Michal Paulovic, Feb 17 2024
If it exists, a(8) > 6*10^4. - Kellen Shenton, Dec 21 2024
EXAMPLE
2 is in the sequence because 4! - 2! + 1 = 23 is prime.
7 is in the sequence because 14! - 7! + 1 = 87178286161 is prime.
12 is not in the sequence because 24! - 12! + 1 = 620448401733238960358401 = 587 * 21523 * 49109415278124401.
MATHEMATICA
Select[Range[100], PrimeQ[(2#)! - #! + 1] &] (* Alonso del Arte, Feb 09 2014 *)
PROG
(PARI) for(n = 1, 2500, if(isprime((2*n)! - n! + 1), print1(n, ", ")))
CROSSREFS
Cf. A118812 (corresponding primes).
Sequence in context: A366983 A045377 A180470 * A182415 A275491 A360673
KEYWORD
nonn,hard,more
AUTHOR
Rick L. Shepherd, Feb 07 2014
EXTENSIONS
a(6) from Michal Paulovic, Nov 22 2023
a(7) from Kellen Shenton, Dec 21 2024
STATUS
approved