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
Examples
17 is in the sequence because 2*17!! + 1 = 2*34459425 + 1 = 68918851 is prime.
Programs
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Mathematica
lst={};Do[If[PrimeQ[2*n!!+1],AppendTo[lst,n]],{n,0,1500}];lst -
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
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
Comments