A257864
Numbers n such that n!! - 2^7 is prime.
Original entry on oeis.org
11, 13, 21, 47, 59, 77, 109, 129, 155, 163, 245, 337, 511, 1417, 3013, 3757, 4989, 8977, 12479, 12869
Offset: 1
Cf.
A080778,
A076185,
A076186,
A076188,
A076189,
A076190,
A076193,
A076194,
A076195,
A076196,
A076197 (other forms of n!!+2^k)
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Select[Range[0, 50000], #!! - 128 > 0 && PrimeQ[#!! - 128] &]
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is(n)=ispseudoprime(prod(i=0,(n-1)\2, n-2*i)-128) \\ Charles R Greathouse IV, May 11 2015
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use ntheory ":all"; use Math::GMPz;
sub mf2 { my($n,$P)=(shift,Math::GMPz->new(1)); $P *= $n-($_<<1) for 0..($n-1)>>1; $P; }
for (1..100000) { say if is_prob_prime(mf2($)-128) } # _Dana Jacobsen, May 13 2015
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from gmpy2 import is_prime, mpz
A257864_list, g, h = [], mpz(105), mpz(128)
for i in range(9,10**5,2):
g *= i
if is_prime(g-h):
A257864_list.append(i) # Chai Wah Wu, May 12 2015
A259045
Numbers n such that n!! - 2^6 is prime.
Original entry on oeis.org
7, 9, 11, 17, 21, 27, 29, 39, 43, 45, 67, 145, 173, 613, 833, 1449, 1703, 1719, 2673, 19661, 36095, 37837, 37845
Offset: 1
Cf.
A080778,
A076185,
A076186,
A076188,
A076189,
A076190,
A076193,
A076194,
A076195,
A076196,
A076197 (other forms of n!!+2^k)
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Select[Range[0, 50000], #!! - 64 > 0 && PrimeQ[#!! - 64] &]
Select[Range[4, 6000], PrimeQ[#!! - 64] &] (* Vincenzo Librandi, Jun 18 2015 *)
A374901
Numbers k such that k!^2 + ((k - 1)!^2) + 1 is prime.
Original entry on oeis.org
1, 3, 4, 6, 10, 11, 118, 271, 288, 441, 457, 2931, 5527, 6984, 9998, 10395, 13703
Offset: 1
4 is a term, because 4!^2 + 3!^2 + 1 = 576 + 36 + 1 = 613 is a prime number.
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is(k) = isprime((k!^2)+((k-1)!)^2+1);
-
from itertools import count, islice
from sympy import isprime
def A374901_gen(): # generator of terms
f = 1
for k in count(1):
if isprime((k**2+1)*f+1):
yield k
f *= k**2
A374901_list = list(islice(A374901_gen(),10)) # Chai Wah Wu, Oct 02 2024
A110094
Startorial primes.
Original entry on oeis.org
2, 3, 5, 7, 23, 719, 5039, 1451521, 2903041, 5806081, 46448639, 92897281, 371589121, 10032906239, 30098718719, 270888468479, 812665405439, 7313988648961, 21941965946881, 89874292518420479
Offset: 1
A274385
Double factorial primes: primes which are within 1 of a double factorial number.
Original entry on oeis.org
2, 3, 7, 47, 383, 10321919, 51011754393599, 1130138339199322632554990773529330319359999999, 73562883979319395645666688474019139929848516028923903999999999, 4208832729023498248022825567687608993477547383960134557368319999999999
Offset: 1
a(2) = 3 = 2 + 1 = 2!! + 1 is the 2nd prime of that form.
a(4) = 47 = 2*4*6 - 1 = 6!! - 1 is the 4th prime of that form.
-
r:=91; I:=[1, 1]; lst1:=[n le 2 select I[n] else (n-1)*Self(n-2): n in [1..r]]; lst2:=[]; for c in [1..r] do a:=lst1[c]; for s in [-1..1 by 2] do p:=a+s; if IsPrime(p) and not p in lst2 then Append(~lst2, p); end if; end for; end for; lst2;
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