A215775 Numbers k such that 2*k!! + 1 is a prime.

0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 13, 17, 18, 24, 28, 30, 39, 51, 149, 197, 355, 444, 623, 908, 1084, 1125, 1577, 1748, 2584, 2628, 2702, 3973, 5046, 6048, 6058, 7123, 9706, 14223, 17775

Offset

1,3

Comments

The corresponding primes are in A215777.

Links

Table of n, a(n) for n=1..39.

Example

17 is in the sequence because 2*17!! + 1 = 2*34459425 + 1 = 68918851 is prime.

Mathematica

lst={}; Do[If[PrimeQ[2*n!!+1], AppendTo[lst, n]], {n, 0, 1500}]; lst

Prog

(Python)
from sympy import isprime
def afind(startat=0, limit=10**9):
  df, dfm1 = 1, 1
  for k in range(startat):
    df, dfm1 = (k+1)*dfm1, df
  for k in range(startat, limit+1):
    if isprime(2*df+1): print(k, end=", ")
    df, dfm1 = (k+1)*dfm1, df
afind(limit=625) # Michael S. Branicky, May 16 2021

Crossrefs

Cf. A006882, A215777.

Sequence in context: A061920 A062010 A071218 * A363149 A236310 A005709

Adjacent sequences: A215772 A215773 A215774 * A215776 A215777 A215778

Keyword

nonn,hard,more

Author

Michel Lagneau, Aug 23 2012

Extensions

Offset changed to 1 by and a(29)-a(31) from Jinyuan Wang, May 15 2021

a(32)-a(33) from Michael S. Branicky, May 16 2021

a(34)-a(39) from Michael S. Branicky, Aug 13 2024

Status

approved