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Search: a126896 -id:a126896
Displaying 1-9 of 9 results found.
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A139056
Numbers k for which (k!-3)/3 is prime.
+10
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
A051915
Numbers k such that 2*k! + 1 is prime.
+10
12
0, 1, 2, 3, 5, 12, 18, 35, 51, 53, 78, 209, 396, 4166, 9091, 9587, 13357, 15917, 17652, 46127
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Used PrimeForm to prove primality for n = 4166 (classical N-1 test). - David Radcliffe, May 28 2007
LINKS
Table of n, a(n) for n=1..20.
EXAMPLE
k = 5 is here because 2*5! + 1 = 241 is prime.
MATHEMATICA
Select[Range[0, 400], PrimeQ[2*#! + 1] &] (* Vladimir Joseph Stephan Orlovsky, Feb 13 2012 *)
PROG
(Magma) [n: n in [0..1000] | IsPrime(2*Factorial(n) +1)]; // Vincenzo Librandi, Feb 21 2015
(PARI) is(k) = ispseudoprime(2*k!+1); \\ Jinyuan Wang, Feb 05 2020
CROSSREFS
Cf. A002981, A076679, A076680, A076681, A076682, A076683, A178488, A180626, A126896.
KEYWORD
nonn,more
AUTHOR
Labos Elemer, Dec 18 1999
EXTENSIONS
4166 from David Radcliffe, May 28 2007
More terms from Serge Batalov, Feb 18 2015
STATUS
approved
A076680
Numbers k such that 4*k! + 1 is prime.
+10
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
A076679
Numbers k such that 3*k! + 1 is prime.
+10
9
2, 3, 4, 6, 7, 9, 10, 13, 23, 25, 32, 38, 40, 47, 96, 3442, 4048, 4522, 4887, 7033, 9528, 12915, 31762
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
a(24) > 50000. - Roger Karpin, Nov 13 2016
LINKS
Table of n, a(n) for n=1..23.
EXAMPLE
k = 6 is here because 3*6! + 1 = 2161 is prime.
PROG
(PARI) isok(n) = isprime(3*n! + 1); \\ Michel Marcus, Nov 13 2016
(PFGW) ABC2 3*$a!+1
a: from 1 to 1000 // Jinyuan Wang, Feb 05 2020
CROSSREFS
Cf. A002981, A051915, A076680, A076681, A076682, A076683, A178488, A180626, A126896.
KEYWORD
nonn,more
AUTHOR
Phillip L. Poplin (plpoplin(AT)bellsouth.net), Oct 25 2002
EXTENSIONS
More terms from Serge Batalov, Feb 18 2015
a(20)-a(23) from Roger Karpin, Nov 13 2016
STATUS
approved
A076683
Numbers k such that 7*k! + 1 is prime.
+10
9
3, 7, 8, 15, 19, 29, 36, 43, 51, 158, 160, 203, 432, 909, 1235, 3209, 8715, 9707
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
a(17) > 5830. - Jinyuan Wang, Feb 05 2020
a(19) > 12000. - Michael S. Branicky, Jul 04 2024
LINKS
Table of n, a(n) for n=1..18.
EXAMPLE
k = 3 is here because 7*3! + 1 = 43 is prime.
PROG
(PARI) is(k) = ispseudoprime(7*k!+1); \\ Jinyuan Wang, Feb 05 2020
(Python)
from sympy import isprime
from math import factorial
def aupto(m): return [k for k in range(m+1) if isprime(7*factorial(k)+1)]
print(aupto(300)) # Michael S. Branicky, Mar 07 2021
CROSSREFS
Cf. A002981, A051915, A076679, A076680, A076681, A076682, A178488, A180626, A126896.
KEYWORD
nonn,more
AUTHOR
Phillip L. Poplin (plpoplin(AT)bellsouth.net), Oct 25 2002
EXTENSIONS
a(17)-a(18) from Michael S. Branicky, Jul 04 2024
STATUS
approved
A178488
Numbers k such that 8*k! + 1 is prime.
+10
9
2, 4, 9, 10, 11, 12, 15, 25, 31, 46, 53, 78, 318, 615, 955, 1646, 2669, 2672, 3515, 7689
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
a(20) > 3810. - Jinyuan Wang, Feb 05 2020
a(21) > 12000. - Michael S. Branicky, Jul 03 2024
LINKS
Table of n, a(n) for n=1..20.
Index entries for sequences related to numbers of primes of the form k*n!+-1
MATHEMATICA
fQ[n_] := PrimeQ[8 n! + 1]; k = 0; lst = {}; While[k < 1501, If[ fQ@k, AppendTo[lst, k]; Print@k]; k++ ]; lst
PROG
(PARI) for(k=1, 999, ispseudoprime(8*k!+1) & print1(k, ", "))
(PFGW) ABC2 8*$a!+1
a: from 1 to 1000 // Jinyuan Wang, Feb 05 2020
CROSSREFS
Cf. A002981, A051915, A076679, A076680, A076681, A076682, A076683, A180626, A126896.
KEYWORD
nonn,hard,more
AUTHOR
Robert G. Wilson v, Sep 13 2010 and M. F. Hasler, Sep 16 2010
EXTENSIONS
a(16)-a(19) from Jinyuan Wang, Feb 05 2020
a(20) from Michael S. Branicky, Jul 02 2024
STATUS
approved
A180626
Numbers k such that 9*k! + 1 is prime.
+10
9
2, 6, 7, 10, 13, 15, 24, 29, 33, 44, 98, 300, 548, 942, 1099, 1176, 1632, 1794, 3676, 3768, 4804, 6499, 8049, 8164, 8917, 10270, 11610, 11959
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Tested to 4500. - Robert G. Wilson v, Sep 28 2010
a(22) > 5235. - Jinyuan Wang, Feb 05 2020
LINKS
Table of n, a(n) for n=1..28.
Index entries for sequences related to numbers of primes of the form k*n!+-1
MATHEMATICA
fQ[n_] := PrimeQ[9 n! + 1]; k = 0; lst = {}; While[k < 1501, If[ fQ@k, AppendTo[lst, k]; Print@k]; k++ ]; lst
PROG
(PARI) is(k) = ispseudoprime(9*k!+1); \\ Jinyuan Wang, Feb 05 2020
CROSSREFS
Cf. A002981, A051915, A076679, A076680, A076681, A076682, A076683, A178488, A126896.
KEYWORD
nonn,more
AUTHOR
Robert G. Wilson v, Sep 13 2010
EXTENSIONS
a(17)-a(20) from Robert G. Wilson v, Sep 28 2010
a(21) from Jinyuan Wang, Feb 05 2020
a(22) from Michael S. Branicky, May 27 2023
a(23)-a(28) from Michael S. Branicky, Jul 12 2024
STATUS
approved
A076681
Numbers k such that 5*k! + 1 is prime.
+10
7
2, 3, 5, 10, 11, 12, 17, 34, 74, 136, 155, 259, 271, 290, 352, 479, 494, 677, 776, 862, 921, 932, 2211, 3927, 4688, 12567
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
a(26) > 4700. - Jinyuan Wang, Feb 04 2020
LINKS
Table of n, a(n) for n=1..26.
EXAMPLE
k = 3 is here because 5*3! + 1 = 31 is prime.
PROG
(PARI) is(k) = ispseudoprime(5*k!+1); \\ Jinyuan Wang, Feb 04 2020
CROSSREFS
Cf. A002981, A051915, A076679, A076680, A076682, A076683, A178488, A180626, A126896.
KEYWORD
nonn,more
AUTHOR
Phillip L. Poplin (plpoplin(AT)bellsouth.net), Oct 25 2002
EXTENSIONS
a(25) from Jinyuan Wang, Feb 04 2020
a(26) from Michael S. Branicky, Jul 03 2024
STATUS
approved
A076682
Numbers k such that 6*k! + 1 is prime.
+10
7
0, 1, 2, 3, 7, 8, 9, 12, 13, 18, 24, 38, 48, 60, 113, 196, 210, 391, 681, 739, 778, 1653, 1778, 1796, 1820, 2391, 2505, 4595, 8937
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
a(29) > 5800. - Jinyuan Wang, Feb 05 2020
a(30) > 12000. - Michael S. Branicky, Jul 04 2024
LINKS
Table of n, a(n) for n=1..29.
EXAMPLE
k = 3 is here because 6*3! + 1 = 37 is prime.
PROG
(PARI) is(k) = ispseudoprime(6*k!+1); \\ Jinyuan Wang, Feb 05 2020
CROSSREFS
Cf. A002981, A051915, A076679, A076680, A076681, A076683, A178488, A180626, A126896.
KEYWORD
nonn,more
AUTHOR
Phillip L. Poplin (plpoplin(AT)bellsouth.net), Oct 25 2002
EXTENSIONS
a(26) inserted by and a(29) from Michael S. Branicky, Jul 03 2024
STATUS
approved
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