A080778 Double factorial primes; values k for which k!! + 1 is prime.

0, 1, 2, 518, 33416, 37310, 52608, 123998, 220502

Offset: 1

Author

Steven Harvey, Mar 11 2003

Keywords

• hard
• nonn
• more

Comments

Numbers k such that A006882(k) + 1 is prime.

a(1) and a(2) correspond to the same prime, 1+1. For n >= 3, a(n) is even (because (2j+1)!! + 1 is even), and then a(n)/2 equals A256594(n-1). - Jeppe Stig Nielsen, Apr 01 2023

Examples

			518 is included because 518*516*514*...*4*2 + 1 is prime. - _Jeppe Stig Nielsen_, Apr 01 2023
		

Links

• Ken Davis, Status of Search for Multifactorial Primes.
• Ken Davis, Results for n!2+1.
• Shyam Sunder Gupta, Fascinating Factorials, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 16, 411-442.
• Eric Weisstein's World of Mathematics, Double Factorial Prime
• Eric Weisstein's World of Mathematics, Integer Sequence Primes

Crossrefs

Cf. A006882, A007749, A256594.

Extensions

a(7) from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008

a(8) from Sou Fukui, Jun 05 2015

a(9) from Sou Fukui, Jan 17 2017