A076679 -id:A076679 - cp's OEIS frontend

A139056 Numbers k for which (k!-3)/3 is prime.

4, 6, 12, 16, 29, 34, 43, 111, 137, 181, 528, 2685, 39477, 43697

Offset: 1

Artur Jasinski, Apr 07 2008

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

C. Caldwell. The Prime database entry for the prime generated by a(i)=98166.

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.

a = {}; Do[If[PrimeQ[(-3 + n!)/3], AppendTo[a, n]], {n, 1, 1000}]; a

for(n=1,1000,if(floor(n!/3-1)==n!/3-1,if(ispseudoprime(n!/3-1),print(n)))) \\ Derek Orr, Mar 28 2014

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

A051915 Numbers k such that 2*k! + 1 is prime.

Original entry on oeis.org

0, 1, 2, 3, 5, 12, 18, 35, 51, 53, 78, 209, 396, 4166, 9091, 9587, 13357, 15917, 17652, 46127, 66480

Offset: 1

Labos Elemer, Dec 18 1999

Used PrimeForm to prove primality for n = 4166 (classical N-1 test). - David Radcliffe, May 28 2007

a(22) > 80000. - Serge Batalov, Jun 09 2025

			k = 5 is here because 2*5! + 1 = 241 is prime.

Cf. A002981, A076679, A076680, A076681, A076682, A076683, A178488, A180626, A126896.

[n: n in [0..1000] | IsPrime(2*Factorial(n) +1)]; // Vincenzo Librandi, Feb 21 2015

Select[Range[0, 400], PrimeQ[2*#! + 1] &] (* Vladimir Joseph Stephan Orlovsky, Feb 13 2012 *)

is(k) = ispseudoprime(2*k!+1); \\ Jinyuan Wang, Feb 05 2020

4166 from David Radcliffe, May 28 2007
More terms from Serge Batalov, Feb 18 2015
a(21) from Serge Batalov, Jun 08 2025

A076680 Numbers k such that 4*k! + 1 is prime.

Original entry on oeis.org

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

Offset: 1

Phillip L. Poplin (plpoplin(AT)bellsouth.net), Oct 25 2002

a(25) > 6311. - Jinyuan Wang, Feb 06 2020

			k = 7 is a term because 4*7! + 1 = 20161 is prime.

Factor Database, Factors of the numbers 4z!+1

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.

Select[Range[5000],PrimeQ[4#!+1]&] (* Harvey P. Dale, Mar 23 2011 *)

is(k) = ispseudoprime(4*k!+1); \\ Jinyuan Wang, Feb 06 2020

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

A126896 Numbers k such that 10*k! + 1 is prime.

Original entry on oeis.org

0, 1, 3, 4, 5, 23, 32, 39, 61, 349, 718, 805, 1025, 1194, 1550, 1774, 3417, 7583

Offset: 1

Parthasarathy Nambi, May 07 2007

a(17) > 2880. - Jinyuan Wang, Feb 05 2020

a(19) > 12000. - Michael S. Branicky, Jul 07 2024

			k = 4 is a term because 10*4! + 1 = 241 is prime.

Corresponding primes are in A089764.

Cf. A002981, A051915, A076679, A076680, A076681, A076682, A076683, A178488, A180626.

is(k) = ispseudoprime(10*k!+1); \\ Jinyuan Wang, Feb 05 2020

a(15)-a(16) from Jinyuan Wang, Feb 05 2020
a(17) from Michael S. Branicky, Apr 16 2023
a(18) from Michael S. Branicky, Jul 07 2024

A076683 Numbers k such that 7*k! + 1 is prime.

Original entry on oeis.org

3, 7, 8, 15, 19, 29, 36, 43, 51, 158, 160, 203, 432, 909, 1235, 3209, 8715, 9707

Offset: 1

Phillip L. Poplin (plpoplin(AT)bellsouth.net), Oct 25 2002

a(17) > 5830. - Jinyuan Wang, Feb 05 2020

a(19) > 12000. - Michael S. Branicky, Jul 04 2024

			k = 3 is here because 7*3! + 1 = 43 is prime.

Cf. A002981, A051915, A076679, A076680, A076681, A076682, A178488, A180626, A126896.

is(k) = ispseudoprime(7*k!+1); \\ Jinyuan Wang, Feb 05 2020

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

a(17)-a(18) from Michael S. Branicky, Jul 04 2024

A178488 Numbers k such that 8*k! + 1 is prime.

Original entry on oeis.org

2, 4, 9, 10, 11, 12, 15, 25, 31, 46, 53, 78, 318, 615, 955, 1646, 2669, 2672, 3515, 7689

Offset: 1

Robert G. Wilson v, Sep 13 2010 and M. F. Hasler, Sep 16 2010

a(20) > 3810. - Jinyuan Wang, Feb 05 2020

a(21) > 12000. - Michael S. Branicky, Jul 03 2024

Index entries for sequences related to numbers of primes of the form k*n!+-1

Cf. A002981, A051915, A076679, A076680, A076681, A076682, A076683, A180626, A126896.

fQ[n_] := PrimeQ[8 n! + 1]; k = 0; lst = {}; While[k < 1501, If[ fQ@k, AppendTo[lst, k]; Print@k]; k++ ]; lst

for(k=1, 999, ispseudoprime(8*k!+1) & print1(k, ", "))

ABC2 8*$a!+1
a: from 1 to 1000 // Jinyuan Wang, Feb 05 2020

a(16)-a(19) from Jinyuan Wang, Feb 05 2020

a(20) from Michael S. Branicky, Jul 02 2024

A180626 Numbers k such that 9*k! + 1 is prime.

Original entry on oeis.org

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

Offset: 1

Robert G. Wilson v, Sep 13 2010

Tested to 4500. - Robert G. Wilson v, Sep 28 2010

a(22) > 5235. - Jinyuan Wang, Feb 05 2020

Index entries for sequences related to numbers of primes of the form k*n!+-1

Cf. A002981, A051915, A076679, A076680, A076681, A076682, A076683, A178488, A126896.

fQ[n_] := PrimeQ[9 n! + 1]; k = 0; lst = {}; While[k < 1501, If[ fQ@k, AppendTo[lst, k]; Print@k]; k++ ]; lst

is(k) = ispseudoprime(9*k!+1); \\ Jinyuan Wang, Feb 05 2020

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

A076682 Numbers k such that 6*k! + 1 is prime.

Original entry on oeis.org

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

Offset: 1

Phillip L. Poplin (plpoplin(AT)bellsouth.net), Oct 25 2002

a(29) > 5800. - Jinyuan Wang, Feb 05 2020

a(30) > 12000. - Michael S. Branicky, Jul 04 2024

			k = 3 is here because 6*3! + 1 = 37 is prime.

Cf. A002981, A051915, A076679, A076680, A076681, A076683, A178488, A180626, A126896.

is(k) = ispseudoprime(6*k!+1); \\ Jinyuan Wang, Feb 05 2020

a(26) inserted by and a(29) from Michael S. Branicky, Jul 03 2024

A076681 Numbers k such that 5*k! + 1 is prime.

Original entry on oeis.org

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

Offset: 1

Phillip L. Poplin (plpoplin(AT)bellsouth.net), Oct 25 2002

a(26) > 4700. - Jinyuan Wang, Feb 04 2020

			k = 3 is here because 5*3! + 1 = 31 is prime.

Cf. A002981, A051915, A076679, A076680, A076682, A076683, A178488, A180626, A126896.

is(k) = ispseudoprime(5*k!+1); \\ Jinyuan Wang, Feb 04 2020

a(25) from Jinyuan Wang, Feb 04 2020

a(26) from Michael S. Branicky, Jul 03 2024

A062551 Primes of the form 3*k! + 1.

Original entry on oeis.org

7, 19, 73, 2161, 15121, 1088641, 10886401, 18681062401, 77556050216654929920001, 46533630129992957952000001, 789392510801080590501654036480000001

Offset: 1

Jason Earls, Jul 10 2001

nonn

Harry J. Smith, Table of n, a(n) for n=1,...,15

Cf. A076679, A173324.

lst={};Do[p=3*n!+1;If[PrimeQ[p],AppendTo[lst,p]],{n,0,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 28 2009 *)
Select[3*Range[40]! +1,PrimeQ] (* Harvey P. Dale, Jul 20 2018 *)

for(n=1,40, if(isprime(3*n!+1),print(3*n!+1)))

{ n=0; for (m=0, 10^5, if(isprime(a=3*m! + 1), write("b062551.txt", n++, " ", a); if (n==15, break)) ) } \\ Harry J. Smith, Aug 08 2009

a(n) = A173324(A076679(n)). - Elmo R. Oliveira, Apr 17 2025

cp's OEIS Frontend

A139056 Numbers k for which (k!-3)/3 is prime.

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A051915 Numbers k such that 2*k! + 1 is prime.

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A076680 Numbers k such that 4*k! + 1 is prime.

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A126896 Numbers k such that 10*k! + 1 is prime.

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A076683 Numbers k such that 7*k! + 1 is prime.

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A178488 Numbers k such that 8*k! + 1 is prime.

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PFGW

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A180626 Numbers k such that 9*k! + 1 is prime.

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