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Double factorial primes; values k for which k!! + 1 is prime.
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%I #41 Apr 01 2023 22:05:11

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

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

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

%C 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

%H Ken Davis, <a href="http://mfprimes.free-dc.org">Status of Search for Multifactorial Primes.</a>

%H Ken Davis, <a href="http://mfprimes.free-dc.org/mfdata/f02p.html">Results for n!2+1.</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DoubleFactorialPrime.html">Double Factorial Prime</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>

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

%Y Cf. A006882, A007749, A256594.

%K hard,nonn,more

%O 1,3

%A _Steven Harvey_, Mar 11 2003

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

%E a(8) from _Sou Fukui_, Jun 05 2015

%E a(9) from _Sou Fukui_, Jan 17 2017