A274386 - OEIS

%I #13 Sep 08 2022 08:46:17

%S 2,3,5,11,17,19,29,79,163,281,881,209441,4188799,264539521,2504902399,

%T 72642169601,254561089305599,9927882482918401,26582634158080001,

%U 13106744139423334399999,141383412854531380076544001,427380210218181008588800001

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

%C Union of A037082 and A135726.

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>

%e a(7) = 29 = 4*7 + 1 = 7!!! + 1 is the 7th prime of that form.

%e a(8) = 79 = 2*5*8 - 1 = 8!!! - 1 is the 8th prime of that form.

%t 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 *)

%t Select[Union[Flatten[#+{1,-1}&/@Table[Times@@Range[n,1,-3],{n,100}]]],PrimeQ] (* _Harvey P. Dale_, Sep 05 2022 *)

%o (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;

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

%K nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Jun 19 2016