A215912 Primes of the form 2*!k + 1.

3, 3, 5, 19, 89, 3709, 266993, 15394128503491

Offset

1,1

Comments

!n is a subfactorial number (A000166).

The corresponding k are {0, 2, 3, 4, 5, 7, 9, 16, 88, ...}. The next prime of this sequence contains 135 digits.

Links

Table of n, a(n) for n=1..8.

Example

The prime 3709 = 2*!7 + 1 = 2*1854 + 1 is in the sequence.

Maple

with(numtheory): f:=n->sum(n!*(((-1)^k)*1/k!), k=0..n):for n from 1 to 150 do: if type(2*f(n)+1, prime) = true then printf(`%d, `, 2*f(n)+1):else fi:od:

Mathematica

  a={}; Do[p= 2* Subfactorial[n]+1; If[PrimeQ[p], AppendTo[a, p]], {n, 0, 800}]; Print[a];

Crossrefs

Cf. A000166, A006882.

Sequence in context: A144423 A128636 A123633 * A157241 A365083 A196430

Adjacent sequences: A215909 A215910 A215911 * A215913 A215914 A215915

Keyword

nonn

Author

Michel Lagneau, Aug 26 2012

Status

approved