A180631 -id:A180631 - 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

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

A076133 Numbers k such that 2*k! - 1 is prime.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 14, 15, 17, 22, 28, 91, 253, 257, 298, 659, 832, 866, 1849, 2495, 2716, 2773, 2831, 3364, 5264, 7429, 28539, 32123, 37868, 65591, 113920

Offset: 1

Phillip L. Poplin (plpoplin(AT)bellsouth.net), Oct 30 2002

a(32) > 116000. - Serge Batalov, Jun 06 2025

			k = 5 is here because 2*5! - 1 = 239 is prime.

Cf. A051915.

Cf. A002982, A076134, A099350, A099351, A180627, A180628, A180629, A180630, A180631.

[n: n in [1..600] | IsPrime(2*Factorial(n)-1)]; // Vincenzo Librandi, Feb 20 2015

Select[Range[8000], PrimeQ[2 #! - 1] &] (* Vincenzo Librandi, Feb 20 2015 *)

is(k) = ispseudoprime(2*k!-1); \\ Jinyuan Wang, Feb 04 2020

a(24)-a(29) from Serge Batalov, Feb 18 2015
a(30) from Serge Batalov, Jun 03 2025
a(31) from Serge Batalov, Jun 06 2025

A076134 Numbers k such that 3*k! - 1 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 9, 12, 17, 26, 76, 379, 438, 1695, 6709, 13313, 18504, 19021, 24488, 45552, 49085, 65451

Offset: 1

Phillip L. Poplin (plpoplin(AT)bellsouth.net), Oct 30 2002

a(23) > 80000. - Serge Batalov, Jun 09 2025

			k = 5 is here because 3*5! - 1 = 359 is prime.

Cf. A051915, A076134.

Cf. A002982, A076133, A099350, A099351, A180627, A180628, A180629, A180630, A180631.

for n from 0 to 1000 do if isprime(3*n! - 1) then print(n) end if end do;

Select[Range[0, 10^3], PrimeQ[3 #! - 1] &] (* Robert Price, May 27 2019 *)

isok(n) = isprime(3*n! - 1); \\ Michel Marcus, Nov 13 2016

ABC2 3*$a!+1
a: from 1 to 1000 // Jinyuan Wang, Feb 04 2020

a(15)-a(21) from Roger Karpin, Nov 13 2016

a(22) from Serge Batalov, Jun 08 2025

A099350 Numbers k such that 4*k! - 1 is prime.

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 10, 11, 51, 63, 197, 313, 579, 1264, 2276, 2669, 4316, 4382, 4678, 7907, 10843

Offset: 1

Brian Kell, Oct 12 2004

a(19) > 4570. - Jinyuan Wang, Feb 04 2020

			k = 5 is here because 4*5! - 1 = 479 is prime.

Cf. A076680.

Cf. A002982, A076133, A076134, A099351, A180627, A180628, A180629, A180630, A180631.

for n from 0 to 1000 do if isprime(4*n! - 1) then print(n) end if end do;

For[n = 0, True, n++, If[PrimeQ[4 n! - 1], Print[n]]] (* Jean-François Alcover, Sep 23 2015 *)

is_A099350(n)=ispseudoprime(n!*4-1) \\ M. F. Hasler, Sep 20 2015

a(14) from Alois P. Heinz, Sep 21 2015
a(15)-a(16) from Jean-François Alcover, Sep 23 2015
a(17)-a(18) from Jinyuan Wang, Feb 04 2020
a(19) from Michael S. Branicky, May 16 2023
a(20)-a(21) from Michael S. Branicky, Jul 11 2024

A099351 Numbers k such that 5*k! - 1 is prime.

Original entry on oeis.org

3, 5, 8, 13, 20, 25, 51, 97, 101, 241, 266, 521, 1279, 1750, 2204, 2473, 4193, 5181, 10080

Offset: 1

Brian Kell, Oct 12 2004

a(15) > 1879. - Jinyuan Wang, Feb 04 2020

a(17) > 3500. - Michael S. Branicky, Mar 06 2021

			k = 5 is here because 5*5! - 1 = 599 is prime.

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

Cf. A002982, A076133, A076134, A099350, A180627, A180628, A180629, A180630, A180631.

for n from 0 to 1000 do if isprime(5*n! - 1) then print(n) end if end do;

Select[Range[550],PrimeQ[5#!-1]&] (* Harvey P. Dale, Nov 27 2013 *)

is(n)=ispseudoprime(5*n!-1) \\ Charles R Greathouse IV, Jun 13 2017

from sympy import isprime
from math import factorial
print([k for k in range(300) if isprime(5*factorial(k) - 1)]) # Michael S. Branicky, Mar 05 2021

a(13)-a(14) from Jinyuan Wang, Feb 04 2020
a(15)-a(16) from Michael S. Branicky, Mar 05 2021
a(17)-a(18) from Michael S. Branicky, Apr 03 2023
a(19) from Michael S. Branicky, Jul 12 2024

A180627 Numbers k such that 6*k! - 1 is prime.

Original entry on oeis.org

0, 1, 2, 5, 8, 42, 318, 326, 1054, 2987, 11243

Offset: 1

Robert G. Wilson v, Sep 13 2010

Tested to 4400. - Robert G. Wilson v, Sep 28 2010

a(11) > 6300. - Jinyuan Wang, Feb 04 2020

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

Cf. A002982, A076133, A076134, A099350, A099351, A180628, A180630, A180630, A180631.

fQ[n_] := PrimeQ[6 n! - 1]; k = 0; lst = {}; While[k < 1501, If[ fQ@k, AppendTo[lst, k]; Print@k]; k++ ]; lst

is(k) = ispseudoprime(6*k!-1); \\ Jinyuan Wang, Feb 04 2020

a(10) from Robert G. Wilson v, Sep 28 2010

a(11) from Michael S. Branicky, Jul 04 2024

A180628 Numbers k such that 7*k! - 1 is prime.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 12, 23, 25, 31, 57, 74, 86, 140, 240, 310, 703, 713, 796, 1028, 1102, 1924, 3469, 3990

Offset: 1

Robert G. Wilson v, Sep 13 2010

a(26) > 12000. - Michael S. Branicky, Jul 07 2024

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

Cf. A002982, A076133, A076134, A099350, A099351, A180627, A180629, A180630, A180631.

fQ[n_] := PrimeQ[7 n! - 1]; k = 0; lst = {}; While[k < 1501, If[ fQ@k, AppendTo[lst, k]; Print@k]; k++ ]; lst
Select[Range[4000],PrimeQ[7#!-1]&] (* Harvey P. Dale, Apr 22 2024 *)

is(k) = ispseudoprime(7*k!-1); \\ Jinyuan Wang, Feb 03 2020

a(23) from Jinyuan Wang, Feb 03 2020

a(24)-a(25) from Michael S. Branicky, Apr 25 2023

A180630 Numbers k such that 9*k! - 1 is prime.

Original entry on oeis.org

2, 3, 12, 15, 16, 25, 30, 38, 59, 82, 114, 168, 172, 175, 213, 229, 251, 302, 311, 554, 2538, 3050, 3363, 12316

Offset: 1

Robert G. Wilson v, Sep 13 2010

a(22) > 2575. - Jinyuan Wang, Feb 03 2020

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

Cf. A002982, A076133, A076134, A099350, A099351, A180627, A180628, A180629, A180631.

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 03 2020

a(21) from Jinyuan Wang, Feb 03 2020
a(22)-a(23) from Michael S. Branicky, Apr 25 2023
a(24) from Michael S. Branicky, Nov 02 2024

A180629 Numbers k such that 8*k! - 1 is prime.

Original entry on oeis.org

0, 1, 3, 4, 8, 33, 121, 177, 190, 276, 473, 484, 924, 937, 1722, 2626, 4077, 4464, 6166

Offset: 1

Robert G. Wilson v, Sep 13 2010

Tested to 4700. - Robert G. Wilson v, Sep 27 2010
Tested to 5127. - Jinyuan Wang, Feb 03 2020
Tested to 12000. - Michael S. Branicky, Jul 11 2024

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

Cf. A002982, A076133, A076134, A099350, A099351, A180627, A180628, A180630, A180631.

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

is(k) = ispseudoprime(8*k!-1); \\ Jinyuan Wang, Feb 03 2020

a(15)-a(18) from Robert G. Wilson v, Sep 27 2010

a(19) from Michael S. Branicky, May 27 2023

cp's OEIS Frontend

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

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

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A076133 Numbers k such that 2*k! - 1 is prime.

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Magma

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A076134 Numbers k such that 3*k! - 1 is prime.

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Maple

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PFGW

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A099350 Numbers k such that 4*k! - 1 is prime.

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A099351 Numbers k such that 5*k! - 1 is prime.

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A180627 Numbers k such that 6*k! - 1 is prime.

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