cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 13 results. Next

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

Original entry on oeis.org

4, 6, 12, 16, 29, 34, 43, 111, 137, 181, 528, 2685, 39477, 43697
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

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

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.

Programs

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

Views

Author

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

Keywords

Comments

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

Examples

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

Links

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.

Programs

  • Mathematica
    Select[Range[5000],PrimeQ[4#!+1]&] (* Harvey P. Dale, Mar 23 2011 *)
  • PARI
    is(k) = ispseudoprime(4*k!+1); \\ Jinyuan Wang, Feb 06 2020

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

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

Views

Author

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

Keywords

Comments

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

Examples

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

Crossrefs

Cf. A051915.
Cf. A002982, A076134, A099350, A099351, A180627, A180628, A180629, A180630, A180631.

Programs

  • Magma
    [n: n in [1..600] | IsPrime(2*Factorial(n)-1)]; // Vincenzo Librandi, Feb 20 2015
  • Mathematica
    Select[Range[8000], PrimeQ[2 #! - 1] &] (* Vincenzo Librandi, Feb 20 2015 *)
  • PARI
    is(k) = ispseudoprime(2*k!-1); \\ Jinyuan Wang, Feb 04 2020

Extensions

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

Views

Author

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

Keywords

Comments

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

Examples

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

Crossrefs

Cf. A051915, A076134.
Cf. A002982, A076133, A099350, A099351, A180627, A180628, A180629, A180630, A180631.

Programs

  • Maple
    for n from 0 to 1000 do if isprime(3*n! - 1) then print(n) end if end do;
  • Mathematica
    Select[Range[0, 10^3], PrimeQ[3 #! - 1] &] (* Robert Price, May 27 2019 *)
  • 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 04 2020

Extensions

a(15)-a(21) from Roger Karpin, Nov 13 2016
a(22) from Serge Batalov, Jun 08 2025

A076679 Numbers k such that 3*k! + 1 is prime.

Original entry on oeis.org

2, 3, 4, 6, 7, 9, 10, 13, 23, 25, 32, 38, 40, 47, 96, 3442, 4048, 4522, 4887, 7033, 9528, 12915, 31762, 114482
Offset: 1

Views

Author

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

Keywords

Comments

a(25) > 115000. - Serge Batalov, Jun 15 2025

Examples

			k = 6 is here because 3*6! + 1 = 2161 is prime.

Crossrefs

Cf. A002981, A051915, A076680, A076681, A076682, A076683, A178488, A180626, A126896.

Programs

  • 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

Extensions

More terms from Serge Batalov, Feb 18 2015
a(20)-a(23) from Roger Karpin, Nov 13 2016
a(24) from Serge Batalov, Jun 15 2025

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

Views

Author

Parthasarathy Nambi, May 07 2007

Keywords

Comments

a(17) > 2880. - Jinyuan Wang, Feb 05 2020
a(19) > 12000. - Michael S. Branicky, Jul 07 2024

Examples

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

Crossrefs

Corresponding primes are in A089764.
Cf. A002981, A051915, A076679, A076680, A076681, A076682, A076683, A178488, A180626.

Programs

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

Extensions

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

Views

Author

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

Keywords

Comments

a(17) > 5830. - Jinyuan Wang, Feb 05 2020
a(19) > 12000. - Michael S. Branicky, Jul 04 2024

Examples

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

Crossrefs

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

Programs

  • 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

Extensions

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

Views

Author

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

Keywords

Comments

a(20) > 3810. - Jinyuan Wang, Feb 05 2020
a(21) > 12000. - Michael S. Branicky, Jul 03 2024

Links

Crossrefs

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

Programs

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

Extensions

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

Views

Author

Robert G. Wilson v, Sep 13 2010

Keywords

Comments

Tested to 4500. - Robert G. Wilson v, Sep 28 2010
a(22) > 5235. - Jinyuan Wang, Feb 05 2020

Links

Crossrefs

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

Programs

  • Mathematica
    fQ[n_] := PrimeQ[9 n! + 1]; k = 0; lst = {}; While[k < 1501, If[ fQ@k, AppendTo[lst, k]; Print@k]; k++ ]; lst
  • PARI
    is(k) = ispseudoprime(9*k!+1); \\ Jinyuan Wang, Feb 05 2020

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

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

Views

Author

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

Keywords

Comments

a(29) > 5800. - Jinyuan Wang, Feb 05 2020
a(30) > 12000. - Michael S. Branicky, Jul 04 2024

Examples

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

Crossrefs

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

Programs

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

Extensions

a(26) inserted by and a(29) from Michael S. Branicky, Jul 03 2024
Showing 1-10 of 13 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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