Displaying 1-10 of 19 results found.
Numbers k such that 4*k! + 1 is prime.
+0
11
0, 1, 4, 7, 8, 9, 13, 16, 28, 54, 86, 129, 190, 351, 466, 697, 938, 1510, 2748, 2878, 3396, 4057, 4384, 5534, 7069, 10364
EXAMPLE
k = 7 is a term because 4*7! + 1 = 20161 is prime.
PROG
(PARI) is(k) = ispseudoprime(4*k!+1); \\ Jinyuan Wang, Feb 06 2020
AUTHOR
Phillip L. Poplin (plpoplin(AT)bellsouth.net), Oct 25 2002
EXTENSIONS
Corrected (added missed terms 2748, 2878) by Serge Batalov, Feb 24 2015
Numbers k for which (k!-3)/3 is prime.
+0
56
4, 6, 12, 16, 29, 34, 43, 111, 137, 181, 528, 2685, 39477, 43697
COMMENTS
Corresponding primes (k!-3)/3 are in A139057. a(13) > 10000. The PFGW program has been used to certify all the terms up to a(12), using a deterministic test which exploits the factorization of a(n) + 1. - Giovanni Resta, Mar 28 2014 98166 is a member of the sequence but its index is not yet determined. The interval where sieving and tests were not run is [60000,90000]. - Serge Batalov, Feb 24 2015
MATHEMATICA
a = {}; Do[If[PrimeQ[(-3 + n!)/3], AppendTo[a, n]], {n, 1, 1000}]; a
PROG
(PARI) for(n=1, 1000, if(floor(n!/3-1)==n!/3-1, if(ispseudoprime(n!/3-1), print(n)))) \\ Derek Orr, Mar 28 2014
EXTENSIONS
Definition corrected by Derek Orr, Mar 28 2014
Numbers n such that (5+n!)/5 is prime.
+0
26
7, 9, 11, 14, 19, 23, 45, 121, 131, 194, 735, 751, 1316, 1372, 2084, 2562, 5678, 5758, 12533, 24222
COMMENTS
For primes of the form (5+n!)/5 see A139059.
MATHEMATICA
a = {}; Do[If[PrimeQ[(n! + 5)/5], AppendTo[a, n]], {n, 1, 751}]; a
PROG
(Magma) [ n: n in [5..734] | IsPrime((Factorial(n)+5) div 5) ];
(PARI) A139058(n) = local(k=(n!+5)\5); if(isprime(k), k, 0); for(n=5, 800, if( A139058(n)>0, print1(n, ", ")))
CROSSREFS
Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199- A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).
Numbers k such that (k!-5)/5 is prime.
+0
3
5, 11, 12, 16, 36, 41, 42, 47, 127, 136, 356, 829, 1863, 2065, 2702, 4509, 7498
MATHEMATICA
a = {}; Do[If[PrimeQ[(n! - 5)/5], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a (* Artur Jasinski *)
PROG
(Magma) [n: n in [5..500] | IsPrime((Factorial(n)-5) div 5)]; // Vincenzo Librandi, Nov 21 2016
CROSSREFS
Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199- A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).
Numbers k such that (k! + 3)/3 is prime.
+0
57
3, 5, 6, 8, 11, 17, 23, 36, 77, 93, 94, 109, 304, 497, 1330, 1996, 3027, 3053, 4529, 5841, 20556, 26558, 28167
COMMENTS
a(21) > 20000. The PFGW program has been used to certify all the terms up to a(20), using the "N-1" deterministic test. - Giovanni Resta, Mar 31 2014
PROG
(Magma) [n: n in [0..500] | IsPrime((Factorial(n)+3) div 3)]; // Vincenzo Librandi, Dec 12 2011
CROSSREFS
Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199- A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).
EXTENSIONS
1330 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
Numbers n such that (n!-2)/2 is a prime.
+0
20
3, 4, 5, 6, 9, 31, 41, 373, 589, 812, 989, 1115, 1488, 1864, 1918, 4412, 4686, 5821, 13830
EXAMPLE
(4!-2)/2 = 11 is a prime.
PROG
(PARI) xfactpk(n, k=2) = { for(x=2, n, y = (x!-k)/k; if(isprime(y), print1(x", ")) ) }
(Magma) [n: n in [1..600]| IsPrime((Factorial(n)-2) div 2)]; // Vincenzo Librandi, Feb 18 2015
CROSSREFS
Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199, A139200, A139201, A139202, A139203, A139204, A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071
EXTENSIONS
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
Numbers n such that (n! + 2)/2 is a prime.
+0
56
2, 4, 5, 7, 8, 13, 16, 30, 43, 49, 91, 119, 213, 1380, 1637, 2258, 4647, 9701, 12258
PROG
(PARI) \\ x such that (x!+2)/2 is prime
xfactpk(n, k=2) = { for(x=2, n, y = (x!+k)/k; if(isprime(y), print1(x, ", ")) ) }
(Magma) [ n: n in [1..300] | IsPrime((Factorial(n)+2) div 2) ];
CROSSREFS
Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199- A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).
EXTENSIONS
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
Numbers k for which (9 + k!)/9 is prime.
+0
50
8, 46, 87, 168, 259, 262, 292, 329, 446, 1056, 3562, 11819, 26737
COMMENTS
No other k exists, for k <= 6000. - Dimitris Zygiridis (dmzyg70(AT)gmail.com), Jul 25 2008
The next number in the sequence, if one exists, is greater than 10944. - Robert Price, Mar 16 2010 Borrowing from A139074 another term in this sequence is 26737. There may be others between 10944 and 26737. - Robert Price, Dec 13 2011 There are no other terms for k < 26738. - Robert Price, Feb 10 2012
EXAMPLE
a(11) = 3562 because 3562 is the 11th natural number for which k!/9 + 1 is prime. 3562 is the new term.
MATHEMATICA
a = {}; Do[If[PrimeQ[(n! + 9)/9], AppendTo[a, n]], {n, 1, 500}]; a
CROSSREFS
Cf. A139068 (primes of the form (9 + k!)/9).
EXTENSIONS
a(11) from Dimitris Zygiridis (dmzyg70(AT)gmail.com), Jul 25 2008
Numbers k such that (k!-6)/6 is prime.
+0
3
4, 5, 7, 8, 11, 14, 16, 17, 18, 20, 43, 50, 55, 59, 171, 461, 859, 2830, 3818, 5421, 5593, 10118, 10880, 24350
MAPLE
a:=proc(n) if isprime((1/6)*factorial(n)-1)=true then n else end if end proc: seq(a(n), n=4..500); # Emeric Deutsch, Apr 29 2008
MATHEMATICA
a = {}; Do[If[PrimeQ[(n! - 6)/6], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a (* Artur Jasinski *)
CROSSREFS
Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199- A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1 <= m <= 10).
Primes of the form k! / 4 - 1.
+0
3
5, 29, 179, 1259, 10079, 907199, 326918591999, 1600593426431999, 6463004184721244159999
MATHEMATICA
Select[Table[i! / 4 - 1, {i, 4, 100}], PrimeQ[#]&]
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