A215775 - OEIS

%I #24 Aug 14 2024 01:51:45

%S 0,1,2,3,4,5,6,7,8,10,13,17,18,24,28,30,39,51,149,197,355,444,623,908,

%T 1084,1125,1577,1748,2584,2628,2702,3973,5046,6048,6058,7123,9706,

%U 14223,17775

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

%C The corresponding primes are in A215777.

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

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

%o (Python)

%o from sympy import isprime

%o def afind(startat=0, limit=10**9):

%o   df, dfm1 = 1, 1

%o   for k in range(startat):

%o     df, dfm1 = (k+1)*dfm1, df

%o   for k in range(startat, limit+1):

%o     if isprime(2*df+1): print(k, end=", ")

%o     df, dfm1 = (k+1)*dfm1, df

%o afind(limit=625) # _Michael S. Branicky_, May 16 2021

%Y Cf. A006882, A215777.

%K nonn,hard,more

%O 1,3

%A _Michel Lagneau_, Aug 23 2012

%E Offset changed to 1 by and a(29)-a(31) from _Jinyuan Wang_, May 15 2021

%E a(32)-a(33) from _Michael S. Branicky_, May 16 2021

%E a(34)-a(39) from _Michael S. Branicky_, Aug 13 2024