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Numbers m such that m! + p is a prime, where p is the smallest prime > m.
4

%I #20 Aug 07 2024 15:12:30

%S 0,1,2,3,4,5,6,7,10,33,44,48,52,64,73,92,119,182,487,603,987,4884,

%T 6822,8070,11079

%N Numbers m such that m! + p is a prime, where p is the smallest prime > m.

%C Next term, if it exists, is >4800. - _Ryan Propper_, Jan 02 2007

%C From _Farideh Firoozbakht_, Oct 21 2009: (Start)

%C Numbers corresponding to a(19)-a(24) are probable primes.

%C There is no further term up to 8300. (End)

%e 727 = 6! + 7 is a prime but 8! + 11 is composite hence 6 is a member but 8 is not.

%e 7 is in the sequence because 7!=5040, nextprime(7)=11 and 5040+11 is prime.

%t Do[If[PrimeQ[k!+NextPrime[k]], Print[k]], {k, 0, 1525}] (* _Farideh Firoozbakht_, Feb 26 2004 *)

%Y Cf. A084748, A084750, A092028, A064278, A002981, A151892.

%K nonn,more

%O 1,3

%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 16 2003

%E More terms from _Farideh Firoozbakht_, Feb 26 2004

%E Edited by _N. J. A. Sloane_ at the suggestion of _Artur Jasinski_, Apr 14 2008

%E a(22)-a(24) from _Farideh Firoozbakht_, Oct 21 2009

%E a(25) from _Michael S. Branicky_, Aug 05 2024