A274386 Triple factorial primes: primes which are within 1 of a triple factorial number.

2, 3, 5, 11, 17, 19, 29, 79, 163, 281, 881, 209441, 4188799, 264539521, 2504902399, 72642169601, 254561089305599, 9927882482918401, 26582634158080001, 13106744139423334399999, 141383412854531380076544001, 427380210218181008588800001

Offset: 1

Author

Arkadiusz Wesolowski, Jun 19 2016

Keywords

• nonn

Comments

Union of A037082 and A135726.

Examples

			a(7) = 29 = 4*7 + 1 = 7!!! + 1 is the 7th prime of that form.
a(8) = 79 = 2*5*8 - 1 = 8!!! - 1 is the 8th prime of that form.
		

Links

• Index entries for sequences related to factorial numbers

Crossrefs

Cf. A007661, A037082, A037083, A084438, A135726.

Programs

Magma

r:=59; I:=[1, 1, 2]; lst1:=[n le 3 select I[n] else (n-1)*Self(n-3): n in [1..r]]; lst2:=[]; for c in [1..r] do a:=lst1[c]; for s in [-1..1 by 2] do p:=a+s; if IsPrime(p) and not p in lst2 then Append(~lst2, p); end if; end for; end for; lst2;

Mathematica

Select[Union@ Flatten@ Map[{# - 1, # + 1} &, Table[With[{q = Quotient[n + 2, 3]}, 3^q q! Binomial[n/3, q]], {n, 0, 58}]], PrimeQ] (* Michael De Vlieger, Jun 21 2016, after Jan Mangaldan at A007661 *)
Select[Union[Flatten[#+{1,-1}&/@Table[Times@@Range[n,1,-3],{n,100}]]],PrimeQ] (* Harvey P. Dale, Sep 05 2022 *)