A049433
Numbers k such that k! - (k-1)! - 1 is prime.
Original entry on oeis.org
3, 4, 6, 8, 9, 12, 28, 78, 99, 184, 286, 291, 398, 411, 600, 718, 732, 889, 1963, 2240, 2242, 2533, 8800, 11403, 18335, 20277, 21029
Offset: 1
Paul Jobling (paul.jobling(AT)whitecross.com)
6 is a term since 6! - (6-1)! - 1 = 599 is prime.
Corrected offset, edited definition and a(19)-a(24) from
Donovan Johnson, Dec 18 2009
A096986
Numbers k such that k*k! + (smallest prime > k) is prime.
Original entry on oeis.org
1, 2, 3, 4, 5, 6, 7, 8, 23, 29, 30, 31, 40, 164, 176, 189, 218, 370, 597, 603, 1473, 1901, 2176, 2436, 2548, 2732, 4758, 5574
Offset: 1
8 is in the sequence because 8*8!+ 11 is prime.
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<< NumberTheory`NumberTheoryFunctions`;v={};Do[If[PrimeQ [n*n!+NextPrime[n]], v=Append[v, n];Print[v]], {n, 2400}]
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isok(n) = isprime(n*n! + nextprime(n+1)); \\ Michel Marcus, Sep 13 2018
A049985
Primes of form k! - (k-1)! - 1.
Original entry on oeis.org
3, 17, 599, 35279, 322559, 439084799, 293999475161295508340735999999
Offset: 1
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f[n_]:=n!-n; lst={};Do[If[PrimeQ[f[n+1]-f[n]],AppendTo[lst,f[n+1]-f[n]]],{n,0,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jun 27 2009 *)
Select[#[[2]]-#[[1]]-1&/@Partition[Range[100]!,2,1],PrimeQ] (* Harvey P. Dale, Feb 17 2015 *)
A096985
Numbers k such that k*k! - NextPrime(k) is prime.
Original entry on oeis.org
3, 5, 8, 10, 12, 13, 23, 26, 30, 33, 38, 114, 162, 219, 265, 268, 277, 344, 463, 651, 877, 1128, 2466, 2594, 4828, 6512
Offset: 1
3 is in the sequence because 3*3! - 5 = 13 is prime.
8 is in the sequence because 8*8! - 11 = 322549 is prime.
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<< NumberTheory`NumberTheoryFunctions`;v={};Do[If[PrimeQ [n*n!-NextPrime[n]], v=Append[v, n];Print[v]], {n, 2150}]
Select[Range[900],PrimeQ[# #!-NextPrime[#]]&] (* The program generates the first 21 terms of the sequence. To select more, increase the Range constant but the program may take a long time to run. *) (* Harvey P. Dale, Aug 16 2023 *)
A346168
Primes p such that p*p! - 1 is prime.
Original entry on oeis.org
2, 3, 5, 7, 11, 397, 599, 2239
Offset: 1
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select(p -> isprime(p) and isprime(p*factorial(p) - 1), [$2 .. 600])
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Select[Range[2, 600], PrimeQ[#] && PrimeQ[#*#! - 1] &]
Select[Prime[Range[110]],PrimeQ[# #!-1]&] (* The program generates the first 7 terms of the sequence. *) (* Harvey P. Dale, Feb 12 2025 *)
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a = List(); for(p=2, 600, if(isprime(p) && isprime(p*p!-1), listput(a, p))); a
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[p for p in range(2, 600) if is_prime(p) and is_prime(p*factorial(p) - 1)]
Showing 1-5 of 5 results.
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