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Search: a139199 -id:a139199
Displaying 1-10 of 19 results found.
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A076680
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
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
a(25) > 6311. - Jinyuan Wang, Feb 06 2020
LINKS
Table of n, a(n) for n=1..26.
Factor Database, Factors of the numbers 4z!+1
EXAMPLE
k = 7 is a term because 4*7! + 1 = 20161 is prime.
MATHEMATICA
Select[Range[5000], PrimeQ[4#!+1]&] (* Harvey P. Dale, Mar 23 2011 *)
PROG
(PARI) is(k) = ispseudoprime(4*k!+1); \\ Jinyuan Wang, Feb 06 2020
CROSSREFS
Cf. m*n!-1 is a prime: A076133, A076134, A099350, A099351, A180627-A180631.
Cf. m*n!+1 is a prime: A051915, A076679-A076683, A178488, A180626, A126896.
Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199-A139205.
Cf. n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071.
KEYWORD
nonn,more
AUTHOR
Phillip L. Poplin (plpoplin(AT)bellsouth.net), Oct 25 2002
EXTENSIONS
Corrected (added missed terms 2748, 2878) by Serge Batalov, Feb 24 2015
a(24) from Jinyuan Wang, Feb 06 2020
a(25)-a(26) from Michael S. Branicky, Jul 04 2024
STATUS
approved
A082671
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
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Table of n, a(n) for n=1..19.
EXAMPLE
(4!-2)/2 = 11 is a prime.
MATHEMATICA
Select[Range[0, 14000], PrimeQ[(#! - 2) / 2] &] (* Vincenzo Librandi, Feb 18 2015 *)
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
KEYWORD
hard,more,nonn
AUTHOR
Cino Hilliard, May 18 2003
EXTENSIONS
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
Edited by T. D. Noe, Oct 30 2008
STATUS
approved
A082672
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
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Table of n, a(n) for n=1..19.
MATHEMATICA
Select[Range[10^2], PrimeQ[(#!+2)/2] &] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)
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. A089130.
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).
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, May 18 2003
EXTENSIONS
More terms from Don Reble, Dec 08 2003
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
STATUS
approved
A089085
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
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
LINKS
Table of n, a(n) for n=1..23.
MATHEMATICA
Select[Range[0, 1400], PrimeQ[(#!+3)/3] &] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)
PROG
(Magma) [n: n in [0..500] | IsPrime((Factorial(n)+3) div 3)]; // Vincenzo Librandi, Dec 12 2011
(PARI) is(n)=ispseudoprime(n!\3+1) \\ Charles R Greathouse IV, Mar 21 2013
CROSSREFS
Cf. A089131.
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).
KEYWORD
nonn
AUTHOR
Cino Hilliard, Dec 05 2003
EXTENSIONS
More terms from Don Reble, Dec 06 2003
1330 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
Typo in Mma program corrected by Vincenzo Librandi, Dec 12 2011
a(16)-a(20) from Giovanni Resta, Mar 31 2014
a(21)-a(23) from Serge Batalov, Feb 17 2015
STATUS
approved
A137390
Numbers k for which (9 + k!)/9 is prime.
+0
50
8, 46, 87, 168, 259, 262, 292, 329, 446, 1056, 3562, 11819, 26737
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
LINKS
Table of n, a(n) for n=1..13.
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
PROG
(PARI) for(n=6, 1e4, if(ispseudoprime(n!/9+1), print1(n", "))) \\ Charles R Greathouse IV, Jul 15 2011
(PFGW) ABC2 $a!/9+1
a: from 6 to 1000 // Jinyuan Wang, Feb 04 2020
CROSSREFS
Cf. A139068 (primes of the form (9 + k!)/9).
Cf. k!/m - 1 is a prime: A002982, A082671, A139056, A139199-A139205.
Cf. (m + k!)/m is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A139071.
KEYWORD
nonn,more
AUTHOR
Artur Jasinski, Apr 09 2008
EXTENSIONS
Edited by N. J. A. Sloane, May 15 2008 at the suggestion of R. J. Mathar
a(10) corrected from 1053 to 1056 by Dmitry Kamenetsky, Jul 12 2008
a(11) from Dimitris Zygiridis (dmzyg70(AT)gmail.com), Jul 25 2008
a(12)-a(13) from Robert Price, Feb 10 2012
STATUS
approved
A139056
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
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
LINKS
Table of n, a(n) for n=1..14.
C. Caldwell. The Prime database entry for the prime generated by a(i)=98166.
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
CROSSREFS
Cf. A007749, A117141.
Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199-A139205.
Cf. n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071.
Cf. m*n!-1 is a prime: A076133, A076134, A099350, A099351, A180627-A180631.
Cf. m*n!+1 is a prime: A051915, A076679-A076683, A178488, A180626, A126896.
KEYWORD
nonn,more
AUTHOR
Artur Jasinski, Apr 07 2008
EXTENSIONS
Definition corrected by Derek Orr, Mar 28 2014
a(8)-a(11) from Derek Orr, Mar 28 2014
a(12) from Giovanni Resta, Mar 28 2014
a(13)-a(14) from Serge Batalov, Feb 24 2015
STATUS
approved
A139058
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
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
For primes of the form (5+n!)/5 see A139059.
a(21) > 25000. - Robert Price, Nov 20 2016
LINKS
Table of n, a(n) for n=1..20.
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. A139059.
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).
KEYWORD
nonn
AUTHOR
Artur Jasinski, Apr 07 2008
EXTENSIONS
More terms from Serge Batalov, Feb 18 2015
a(19)-a(20) from Robert Price, Nov 20 2016
STATUS
approved
A139061
Numbers n for which (4+n!)/4 is prime.
+0
25
4, 5, 6, 13, 21, 25, 32, 40, 61, 97, 147, 324, 325, 348, 369, 1290, 1342, 3167, 6612, 8176, 10990
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
For primes of the form (4+k!)/4, see A139060.
a(22) > 25000. - Robert Price, Jan 10 2017
LINKS
Table of n, a(n) for n=1..21.
MATHEMATICA
a = {}; Do[If[PrimeQ[(n! + 4)/4], AppendTo[a, n]], {n, 1, 500}]; a
Select[Range[500], PrimeQ[(4+#!)/4]&] (* Harvey P. Dale, Mar 24 2011 *)
PROG
(PARI) for(n=4, 1e3, if(ispseudoprime(n!/4+1), print1(n", "))) \\ Charles R Greathouse IV, Jul 15 2011
CROSSREFS
Cf. A082672, A089085, A089130, A117141, A007749, A139056, A139057, A139058, A139059, A139060, A139061, A139061, A139062, A139063, A139064, A139065, A139066, A020458, A139068, A137390, A139070, A139071, A139072.
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).
KEYWORD
nonn
AUTHOR
Artur Jasinski, Apr 07 2008
EXTENSIONS
More terms from Serge Batalov, Feb 18 2015
a(19) - a(21) from Robert Price, Jan 10 2017
STATUS
approved
A139063
Numbers k for which (6+k!)/6 is prime.
+0
25
3, 4, 10, 11, 13, 14, 17, 21, 82, 115, 165, 167, 173, 174, 208, 225, 380, 655, 1187, 2000, 2568, 3010, 4542, 8750, 12257, 12601, 24083
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
For primes of the form (6+k!)/6, see A139062.
a(28) > 25000. - Robert Price, Nov 20 2016
LINKS
Table of n, a(n) for n=1..27.
MATHEMATICA
a = {}; Do[If[PrimeQ[(n! + 6)/6], AppendTo[a, n]], {n, 1, 500}]; a
PROG
(PARI) for(k=3, 1e3, if(ispseudoprime(k!/6+1), print1(k", "))) \\ Charles R Greathouse IV, Jul 15 2011
CROSSREFS
Cf. A082672, A089085, A089130, A117141, A007749, A139056, A139057, A139058, A139059, A139060, A139061, A139061, A139062, A139063, A139064, A139065, A139066, A020458.
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).
KEYWORD
nonn
AUTHOR
Artur Jasinski, Apr 07 2008
EXTENSIONS
a(18) and a(19) from Robert Israel, May 19 2014
More terms from Serge Batalov, Feb 18 2015
a(24)-a(27) from Robert Price, Nov 20 2016
STATUS
approved
A139065
Numbers k for which (7+k!)/7 is prime.
+0
25
11, 15, 16, 25, 35, 59, 64, 68, 82, 121, 149, 238, 584, 912, 3349, 4111, 4324, 15314, 19944, 20658, 22740, 23364
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
For primes of the form (7+k!)/7, see A139064.
a(23) > 25000. - Robert Price, Nov 20 2016
LINKS
Table of n, a(n) for n=1..22.
MATHEMATICA
a = {}; Do[If[PrimeQ[(n! + 7)/7], AppendTo[a, n]], {n, 1, 500}]; a
Select[Range[500], PrimeQ[(7+#!)/7]&] (* Harvey P. Dale, Sep 01 2014 *)
PROG
(PARI) for(k=7, 1e3, if(ispseudoprime(k!/7+1), print1(k", "))) \\ Charles R Greathouse IV, Jul 15 2011
CROSSREFS
Cf. A082672, A089085, A089130, A117141, A007749, A139056, A139057, A139058, A139059, A139060, A139061, A139061, A139062, A139063, A139064, A139065, A139066, A020458.
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).
KEYWORD
nonn,hard,more
AUTHOR
Artur Jasinski, Apr 07 2008
EXTENSIONS
More terms from Serge Batalov, Feb 18 2015
a(18)-a(22) from Robert Price, Nov 20 2016
STATUS
approved
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