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A257864 Numbers n such that n!! - 2^7 is prime.

%I A257864 #17 May 22 2025 10:21:42
%S A257864 11,13,21,47,59,77,109,129,155,163,245,337,511,1417,3013,3757,4989,
%T A257864 8977,12479,12869
%N A257864 Numbers n such that n!! - 2^7 is prime.
%C A257864 a(21) > 50000. - _Robert Price_, May 11 2015
%C A257864 a(n) is odd. - _Chai Wah Wu_, May 12 2015
%H A257864 C. K. Caldwell, The Prime Glossary, <a href="https://t5k.org/glossary/page.php/MultifactorialPrime.html">multifactorial prime</a>
%H A257864 Joe McLean, <a href="http://web.archive.org/web/20091027034731/http://uk.geocities.com/nassarawa%40btinternet.com/probprim2.htm">Interesting Sources of Probable Primes</a>
%t A257864 Select[Range[0, 50000], #!! - 128 > 0 && PrimeQ[#!! - 128] &]
%o A257864 (PARI) is(n)=ispseudoprime(prod(i=0,(n-1)\2, n-2*i)-128) \\ _Charles R Greathouse IV_, May 11 2015
%o A257864 (Python)
%o A257864 from gmpy2 import is_prime, mpz
%o A257864 A257864_list, g, h = [], mpz(105), mpz(128)
%o A257864 for i in range(9,10**5,2):
%o A257864     g *= i
%o A257864     if is_prime(g-h):
%o A257864         A257864_list.append(i) # _Chai Wah Wu_, May 12 2015
%o A257864 (Perl)
%o A257864 use ntheory ":all"; use Math::GMPz;
%o A257864 sub mf2 { my($n,$P)=(shift,Math::GMPz->new(1)); $P *= $n-($_<<1) for 0..($n-1)>>1; $P; }
%o A257864 for (1..100000) { say if is_prob_prime(mf2($_)-128) } # _Dana Jacobsen_, May 13 2015
%Y A257864 Cf. A007749, A094144, A123910  (other forms of n!!-2^k)
%Y A257864 Cf. A080778, A076185, A076186, A076188, A076189, A076190, A076193, A076194, A076195, A076196, A076197  (other forms of n!!+2^k)
%K A257864 nonn,hard,more
%O A257864 1,1
%A A257864 _Robert Price_, May 11 2015