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

1,1

Comments

Union of A037082 and A135726.

Links

Table of n, a(n) for n=1..22.

Index entries for sequences related to factorial numbers

Example

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.

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 *)

Prog

(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;

Crossrefs

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

Sequence in context: A362239 A147813 A338578 * A079545 A154755 A040095

Adjacent sequences: A274383 A274384 A274385 * A274387 A274388 A274389

Keyword

nonn

Author

Arkadiusz Wesolowski, Jun 19 2016

Status

approved