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 10 results.

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

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

Views

Author

Labos Elemer, Dec 18 1999

Keywords

Comments

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

Examples

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

Crossrefs

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

Programs

Extensions

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

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

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

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

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

Views

Author

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

Keywords

Comments

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

Examples

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

Crossrefs

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

Programs

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

Extensions

a(25) from Jinyuan Wang, Feb 04 2020
a(26) from Michael S. Branicky, Jul 03 2024

A089764 Primes of the form k! followed by a 1.

Original entry on oeis.org

11, 61, 241, 1201, 258520167388849766400001, 2631308369336935301672180121600000001, 203978820811974433586402817399028973568000000001, 5075802138772247988008568121766252272260045289880360030994059394809856000000000000001
Offset: 1

Views

Author

Amarnath Murthy, Nov 23 2003

Keywords

Comments

The next term has 739 digits. - Harvey P. Dale, Jun 08 2014

Examples

			1201 is a prime obtained as 5! followed by a 1.

Crossrefs

Cf. A089765, A126896.

Programs

  • Mathematica
    Select[Table[FromDigits[Join[IntegerDigits[n!],{1}]],{n,50}],PrimeQ] (* Harvey P. Dale, Jun 08 2014 *)

Extensions

More terms from Lior Manor, May 10 2004
One additional term from Harvey P. Dale, Jun 08 2014
Showing 1-10 of 10 results.

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